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ch._10.docxStatistics for Business and Economics, Ch. 10
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· Caution for Regression Analysis The thread has 4 unread messages.
created by ERIK SEIDEL
Last updated Mar 07, 2015, 8:17 PM
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· Comment on Mar 04, 2015, 5:34 AM
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posted by ERIK SEIDEL at Mar 04, 2015, 5:34 AM
Last updated Mar 04, 2015, 5:34 AM
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When preparing a linear regression analysis, the resulting correlation, or lack of correlation, can be misleading to users. The purpose of a linear regression model is to demonstrate whether an increase or decrease in variable x has a positive or negative impact on variable y. If you see a clear slope that is increasing or decreasing, the logical conclusion is that variable x is directly impacting variable y, or vice versa. However, it is not necessarily true that a change in variable x is the reason for the change in variable y. For example, a study of the impact of drinking more water to someone's level of health may show that drinking more water improves people's health overall. However, it may not be drinking water that is actually improving health. It may be that eating less as a result of drinking more water is actually the cause of the improved health.
· Comment on Mar 05, 2015, 9:43 PM
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posted by ARACHEAL VENTRESS at Mar 05, 2015, 9:43 PM
Last updated Mar 05, 2015, 9:43 PM
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Erik- thanks for your post and your example- relating things to real life examples make the applications more clear. Reading a little further in this week's chapter, there is caution in making inferences based on one variable impacting another.
Our text explains that when using the sample correlation coefficient, r, to infer the nature of the relationship between x and y, two caveats exist: (1) A high correlation does not necessarily imply that a causal relationship exists between x and y− only that a linear trend may exist; (2) a low correlation does not necessarily imply that x and y are unrelated--only that x and y are not strongly linearly related.
Reference
McClave, J. T., Benson, P. G., & Sincich, T. (2011). Statistics for Business and Economics (11th ed.). Boston, MA: Prentice Hal
· Comment on Mar 07, 2015, 5:30 PM
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posted by LOUIS DAILY at Mar 07, 2015, 5:30 PM
Last updated Mar 07, 2015, 5:30 PM
Aracheal,
Yes, some variables are related curvilinearly.
thanks
Lou
· Comment on Mar 07, 2015, 3:11 PM
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posted by DELILAH HENDERSON at Mar 07, 2015, 3:11 PM
Last updated Mar 07, 2015, 3:11 PM
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Erik, that is a good example. Do you think it would help if we were careful to have variable x be as specific as variable y in order for the linear regression analysis to be more true or valid to consumers? Maybe something more defined as the impact of drinking more water to improving kidney function instead of improving someone's level of health overall? Improving someone's level of health seems much broader than the variable of drinking more water.
Your example was really good on showing that just because two variables are put together doesn't necessarily mean that y naturally follows x. I thought this example was along the lines of our first chapter showing some of the surveys that were either skewed or false because of improperly conducting the survey (if one was conducted at all.)
I liked your examples on this post and the one regarding sales and marketing. Thanks for the examples - they help me understand the concept better.
d
· Comment on Mar 07, 2015, 5:31 PM
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posted by LOUIS DAILY at Mar 07, 2015, 5:31 PM
Last updated Mar 07, 2015, 5:31 PM
Delilah,
Finer measurements are always better when constructing a regression line or curve.
thanks
Lou
· Comment on Mar 07, 2015, 5:29 PM
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posted by LOUIS DAILY at Mar 07, 2015, 5:29 PM
Last updated Mar 07, 2015, 5:29 PM
Erik,
Yep "correlation does not imply causation"
thanks
Lou
· Comment on Mar 07, 2015, 8:17 PM
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posted by PATRICIA MARCUS at Mar 07, 2015, 8:17 PM
Last updated Mar 07, 2015, 8:17 PM
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Great post Erik..I agree that when preparing a linear regression analysis the resulting correlation or lack of correlation can be misleading. The regression analysis is a parametric test used for the inference from a dapple to a population. The goal of the regression analysis is to investigate how effective one or more variables are pricing the value of a dependent variable. The relationship between two variables is top establish that changes in the explanatory variable causes changes in the response variable. Even when the strong association is visible the conclusion that the association is due to a casual link bergen the variables is elusive. Correlations and regression only describe linear data and are not resistant. Therefore you should always plot the data before interpreting the regression or correlation.
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Simple Linear Regression The thread has 11 unread messages.
created by LOUIS DAILY
Last updated Mar 07, 2015, 5:53 PM
11
· Comment on Mar 02, 2015, 11:35 AM
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posted by LOUIS DAILY at Mar 02, 2015, 11:35 AM
Last updated Mar 02, 2015, 11:35 AM
You may recall your high school algebra about the equation for a straight line: Y = m X + k where m is the slope of the line and k is the y intercept. Let's say we have two variables X and Y. Let's say they represent height (Y) and weight (X). They can be put into Excel as two columns. We can construct a scatter plot with Excel. The scatter plot will show us the shape of this relationship. The taller you are, on the average, the heavier you are, so there will probably be an upward sloping linear scatter plot. The relationship is not perfect, so you won't be able to draw a line that contains all the points. But what is the best fitting line that we can draw? This assumes of course that a line is in fact a good description of the relationship. The technique of Linear Regression answers this question. Linear Regression will compute the line which best describes the relationship. It does this by computing the slope and intercept of this best fitting line. It is the best fit in the sense that it is the line that is closest on the average to all of the data points (the line of least squares). So we have a "model"--the best description of the relationship between the two variables assuming the relationship is linear (like a line). Can you think of any uses for such a model--for this best fitting line and the equation that describes it?
· Comment on Mar 03, 2015, 5:35 AM
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posted by ERIK SEIDEL at Mar 03, 2015, 5:35 AM
Last updated Mar 03, 2015, 5:35 AM
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Our health insurance company uses regression analysis to review the correlation between various medical expense related metrics. Our actuarial informatics department is probably the heaviest user of regression analysis. For example, regression analysis can be used to determine if certain physical traits or health conditions are related to other health conditions. We may pull together the medical record data from all of our health plan members and look at variables such as high blood pressure and weight. We would chart all members that have blood pressure records above a certain level. The blood pressure readings become the x variable. The y variable would then be the weight of these members. If we see a positive correlation line between weight and high blood pressure, then our medical management department would know to pay particular attention to members which a higher BMI if we are trying to encourage healthy blood pressure of our members.
· Comment on Mar 03, 2015, 8:20 AM
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posted by LOUIS DAILY at Mar 03, 2015, 8:20 AM
Last updated Mar 03, 2015, 8:20 AM
Erik,
Thanks for that inside look. Yes, there are lots and lots of uses for regression.
thanks
Lou
· Comment on Mar 03, 2015, 8:38 PM
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posted by KIM DUNLAP at Mar 03, 2015, 8:38 PM
Last updated Mar 03, 2015, 8:38 PM
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Hi Erik,
Thank you for your example. I always have a much better understanding of topics when I hear how people use them in their everyday work. Linear regression can be used for predictive analysis. Linear regression helps us describe and explain the relationship between one dependent variable and at least one independent variable. According to Statistics Solutions, there are three major uses for linear regression. They are 1) Causal analysis 2) Forecasting and effect and 3) Trend forecasting. One important thing to note is that regression analysis assumes a causal relationship between one or more independent variables and one dependent variable.
https://www.statisticssolutions.com/what-is-linear-regression/
· Comment on Mar 06, 2015, 8:50 AM
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posted by LOUIS DAILY at Mar 06, 2015, 8:50 AM
Last updated Mar 06, 2015, 8:50 AM
Kim,
Regression is mathematically closely related to correlation. While we create causal "models" all the time, we still have to be careful about the direction of causality. Correlation does not imply causation is still the rule.
thanks
Lou
· Comment on Mar 04, 2015, 12:47 PM
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posted by STEPHANIE RECTOR at Mar 04, 2015, 12:47 PM
Last updated Mar 04, 2015, 12:47 PM
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Hello Class,
According to Wikipedia, "In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or moreexplanatory variables (or independent variable) denoted X. The case of one explanatory variable is called simple linear regression . For more than one explanatory variable, the process is called multiple linear regression" (wikipedia, 2015). This type of analysis is used commonly for practical applications. Linear regression requires finding the best-fitting straight line through the data points. A scatter plot is often a useful tool in determining how closely the two variables relate. After reading Eric's response, this reminded me of how my previous sleep company used linear regression in relation to sleep studies. With the research our tech managers implemented into our sleep questionairs, I quickly realized the strong correlation between a patient's BMI (body mass index) and a diagnosis of sleep apnea. The higher a patients BMI was, the more likely they were to be diagnosed with sleep apnea. The obstruction of airways were higher the higher the BMI was. In addition, if untreated with surgery or a CPAP, a patient with sleep apnea had higher increased chances of suffering from severe heart conditions in the longterm.
References:
http://en.wikipedia.org/wiki/Linear_regression
· Comment on Mar 06, 2015, 8:53 AM
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posted by LOUIS DAILY at Mar 06, 2015, 8:53 AM
Last updated Mar 06, 2015, 8:53 AM
Stephanie,
Thanks for sharing that information on your sleep study. That apprently was a correlational study, but correlation is mathematically very related to regression. So...besides calculating the correlation coefficient, there could be a regression line modelling the relationship.
thanks
Lou
· Comment on Mar 05, 2015, 8:48 AM
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posted by CRYSTAL RAMOS at Mar 05, 2015, 8:48 AM
Last updated Mar 05, 2015, 8:48 AM
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In statistics, simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. In other words, simple linear regression fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model (that is, vertical distances between the points of the data set and the fitted line) as small as possible.
The adjective simple refers to the fact that this regression is one of the simplest in statistics. The slope of the fitted line is equal to the correlation between y and x corrected by the ratio of standard deviations of these variables. The intercept of the fitted line is such that it passes through the center of mass (x, y) of the data points.
· Comment on Mar 07, 2015, 5:53 PM
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posted by LOUIS DAILY at Mar 07, 2015, 5:53 PM
Last updated Mar 07, 2015, 5:53 PM
Crystal,
It is "simple" because there is only one independent variable.
thanks
Lou
· Comment on Mar 05, 2015, 7:11 PM
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posted by JUDEENE WALKER at Mar 05, 2015, 7:11 PM
Last updated Mar 05, 2015, 7:11 PM
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HI professor, now that you mention it I do remember the equation for a straight line Y=mX + K. This equation expresses the fact that if we plot y against x, and the variables obey a relationship of this form one will obtain a straight line graph with slope m and an intercept
Simple linear regression is one of the most commonly used techniques for determining how one variable of interest is affected by changes in another variable. From what I remember and read from our text simple linear is used for three main purposes:
a) To predict values of one variable from values of another for which more data are available.
b) To describe the linear dependence of one variable on another
c) To correct for linear dependence of one variable on another
· Comment on Mar 06, 2015, 7:46 PM
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posted by SAID SHEIK ABDI at Mar 06, 2015, 7:46 PM
Last updated Mar 06, 2015, 7:46 PM
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When you think of regression, think prediction. A regression uses the historical relationship between an independent and a dependent variable to predict the future values of the dependent variable. Businesses use regression to predict such things as future sales, stock prices, currency exchange rates, and productivity gains resulting from a training program. Types of Regression A regression models the past relationship between variables to predict their future behavior. As an example, imagine that your company wants to understand how past advertising expenditures have related to sales in order to make future decisions about advertising. The dependent variable in this instance is sales and the independent variable is advertising expenditures.Usually, more than one independent variable influences the dependent variable. You can imagine in the above example that sales are influenced by advertising as well as other factors, such as the number of sales representatives and the commission percentage paid to sales representatives. When one independent variable is used in a regression, it is called a simple regression; when two or more independent variables are used, it is called a multiple regression.
Regression models can be either linear or nonlinear. A linear model assumes the relationships between variables are straight-line relationships, while a nonlinear model assumes the relationships between variables are represented by curved lines. In business you will often see the relationship between the return of an individual stock and the returns of the market modeled as a linear relationship, while the relationship between the price of an item and the demand for it is often modeled as a nonlinear relationship.
http://www.dummies.com/how-to/content/how-to-use-a-linear-regression-to-identify-market-.html
· Comment on Mar 06, 2015, 7:55 PM
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posted by Jynx Gresser at Mar 06, 2015, 7:55 PM
Last updated Mar 06, 2015, 7:55 PM
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I do remember this relationship, specifically y = mx + b and its interpretations with a line graph. Foremost, simple linear regression is a unique concept in statistics and is considered to be "the methodology of estimating and using a straight line relationship" (McClave, Benson, & Sincich, 2011, p. 561). Furthermore, it describes the relationship between the two variables X [independent] and Y [dependent] (California State University-Long Beach, n. d.). The regression equation is written as y= a + bx + e; a or alpha being the constant and b or beta being coefficient of x and the slope of the regression line (California State University-Long Beach, n. d.). There are multiple uses of simple linear regression and they include the effect of pricing on consumer behavior and analyzing the risk involved in business decisions. When companies change prices, they can monitor the amount of product sold with a particular price and then determine the relationship between pricing and purchasing with a linear relationship (Hamel, n. d.). I work in retail and I see this relationship quite frequently, for example, higher prices can reduce the number of clients who purchase the product and lower prices equate to a higher number of purchases. This can help assist with future pricing decisions. Therefore, there is a correlation between these two variables, but it doesn't mean that this is the only cause for this relationship.
References
California State University-Long Beach. (n. d.). Simple regression. Retrieved from http://web.csulb.edu/~msaintg/ppa696/696regs.htm
Hamel, G. (n. d.). What are some ways that linear regression can be applied in business settings?. The Houston Chronicle. Retrieved from http://smallbusiness.chron.com/ways-linear-regression-can-applied-business-settings-35431.html
McClave, J. T., Benson, P. G., & Sincich, T. (2011). Statistics for business and economics (11th ed.). Boston, MA: Prentice Hall. Retrieved from the University of Phoenix eBook Collection database.
Jynx Gresser
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Confidence intervals vs Prediction Intervals The thread has 7 unread messages.
created by ARACHEAL VENTRESS
Last updated Mar 07, 2015, 5:51 PM
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· Comment on Mar 05, 2015, 10:03 PM
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posted by ARACHEAL VENTRESS at Mar 05, 2015, 10:03 PM
Last updated Mar 05, 2015, 10:03 PM
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Confidence intervals tell you about how well you have determined the mean. Assume that the data really are randomly sampled from a Gaussian distribution. If you do this many times, and calculate a confidence interval of the mean from each sample, you'd expect about 95 % of those intervals to include the true value of the population mean. The key point is that the confidence interval tells you about the likely location of the true population parameter.
Prediction intervals tell you where you can expect to see the next data point sampled. Assume that the data really are randomly sampled from a Gaussian distribution. Collect a sample of data and calculate a prediction interval. Then sample one more value from the population. If you do this many times, you'd expect that next value to lie within that prediction interval in 95% of the samples.The key point is that the prediction interval tells you about the distribution of values, not the uncertainty in determining the population mean.
Prediction intervals must account for both the uncertainty in knowing the value of the population mean, plus data scatter. So a prediction interval is always wider than a confidence interval.
Reference
· Comment on Mar 06, 2015, 5:44 AM
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posted by KIM DUNLAP at Mar 06, 2015, 5:44 AM
Last updated Mar 06, 2015, 5:44 AM
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Hii Aracheal,
Thank you for your very clear post on confidence intervals vs. prediction intervals. The other thing I picked up on confidence intervals vs. prediction intervals is that the prediction interval is wider than the confidence interval because the added uncertainty of predicting a single response or point vs. a mean response. For example, I looked at a study where they were predicting the life expectancy of men who smoked 20 cigarettes a day. The confidence interval for the data was (68.70, 77.61) and the prediction interval for the same data was (55.36, 90.95) - a much wider spread.
http://www.real-statistics.com/wp-content/uploads/2012/12/confidence-prediction-intervals-excel.jpg
· Comment on Mar 06, 2015, 7:50 PM
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posted by SAID SHEIK ABDI at Mar 06, 2015, 7:50 PM
Last updated Mar 06, 2015, 7:50 PM
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A prediction interval is an interval associated with a random variable yet to be observed, with a specified probability of the random variable lying within the interval. For example, I might give an 80% interval for the forecast of GDP in 2014. The actual GDP in 2014 should lie within the interval with probability 0.8. Prediction intervals can arise in Bayesian or frequentist statistics.
A confidence interval is an interval associated with a parameter and is a frequentist concept. The parameter is assumed to be non-??random but unknown, and the confidence interval is computed from data. Because the data are random, the interval is random. A 95% confidence interval will contain the true parameter with probability 0.95. That is, with a large number of repeated samples, 95% of the intervals would contain the true parameter.
http://www.real-statistics.com/regression/confidence-and-prediction-intervals/
· Comment on Mar 07, 2015, 9:57 AM
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posted by ERIK SEIDEL at Mar 07, 2015, 9:57 AM
Last updated Mar 07, 2015, 9:57 AM
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I can see the importance of calculating and understanding confidence intervals. There are many uncertainties in the business world, especially in today's fast-paced environment where things change almost every day. When management is preparing to make a strategic decision that will impact a company's future, there will always be some uncertainties. The best managers can do when making decisions is basing those decisions on the best data available. While management cannot be certain about the outcome of a decision, they at least want to be reasonably confident about the success of the project or strategic change in the company. By using data to determine whether there can be 95% certainty of an outcome, management can be confident that the outcome will most likely have the result that is expected.
· Comment on Mar 07, 2015, 2:47 PM
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posted by DELILAH HENDERSON at Mar 07, 2015, 2:47 PM
Last updated Mar 07, 2015, 2:47 PM
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Aracheal, that was a good post telling of the differences between confidence intervals and prediction intervals. I found an article that shows how to calculate the two and showed a two good graphs to help explain the difference. The article, Confidence and prediction intervals for forecasted values, from a website showing how to use Excel, showed that the graph on the left was a confidence interval. It said that with a confidence interval, "This means that there is a 95% probability that the true linear regression line of the population will lie within the confidence interval of the regression line calculated from the sample data.
In the graph on the left of Figure 1, a linear regression line is calculated to fit the sample data points. The confidence interval consists of the space between the two curves (dotted lines). Thus there is a 95% probability that the true best-fit line for the population lies within the confidence interval (e.g. any of the lines in the figure on the right above)." The graph on the right shows the prediction interval. The article mentioned, "There is also a concept called prediction interval. Here we look at any specific value ofx, x0, and find an interval around the predicted value ?0 for x0 such that there is a 95% probability that the real value of y (in the population) corresponding to x0 is within this interval (see the graph on the right side of Figure 1)."
The two graphs helped me understand the two a little better.
Reference:
http://biostatistics/regression/confidence-and-prediction-intervals/
· Comment on Mar 07, 2015, 5:51 PM
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posted by LOUIS DAILY at Mar 07, 2015, 5:51 PM
Last updated Mar 07, 2015, 5:51 PM
Great illustration Delilah,
thanks
Lou
· Comment on Mar 07, 2015, 5:47 PM
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posted by LOUIS DAILY at Mar 07, 2015, 5:47 PM
Last updated Mar 07, 2015, 5:47 PM
Aracheal,
Good job in distinguishing between confidence intervals and prediction intervals
thanks
Lou
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The least square approach The thread has 5 unread messages.
created by ARIEL SMITH
Last updated Mar 07, 2015, 5:38 PM
5
· Comment on Mar 04, 2015, 1:02 PM
Message collapsed. Message unread The least square approach
posted by ARIEL SMITH at Mar 04, 2015, 1:02 PM
Last updated Mar 04, 2015, 1:02 PM
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The least square approach, is a mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve. The sum of the squares of the offsets is used instead of the offset absolute values because this allows the residuals to be treated as a continuous differentiable quantity. However, because squares of the offsets are used, outlying points can have a disproportionate effect on the fit, a property which may or may not be desirable depending on the problem at hand. The linear least squares fitting technique is the simplest and most commonly applied form of linear regression and provides a solution to the problem of finding the best fitting straight line through a set of points. In fact, if the functional relationship between the two quantities being graphed is known to within additive or multiplicative constants, it is common practice to transform the data in such a way that the resulting line is a straight line, say by plotting vs.
instead of
vs.
in the case of analyzing the period
of a pendulum as a function of its length
.
Wolfram Math World. (2013). Retrieved from http://mathworld.wolfram.com/LeastSquaresFitting.html
· Comment on Mar 05, 2015, 7:40 PM
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posted by JUDEENE WALKER at Mar 05, 2015, 7:40 PM
Last updated Mar 05, 2015, 7:40 PM
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After further reading I found that linear regression was the first type of regression analysis to be studied rigorously and used extensively in more practical applications. This is so because models that depend linearly on its unknown parameters are easier o fit than those models which are nonlinearly related to its parameter.
When two variables are highly correlated the points on the scatter diagram more or less follow a diagonal line. What the regression method does is to find the line that minimizes the average distance in the vertical direction from the line to all points. If the goal is forecasting or reduction, linear regression can be used to fit a predictive model to an observed data set of x and y values.
· Comment on Mar 07, 2015, 5:38 PM
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posted by LOUIS DAILY at Mar 07, 2015, 5:38 PM
Last updated Mar 07, 2015, 5:38 PM
Judeene
Good. Just to be exact, the least squares technique minimizes the squared distances, thus "least squares".
thanks
Lou
· Comment on Mar 06, 2015, 8:37 PM
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posted by CRYSTAL RAMOS at Mar 06, 2015, 8:37 PM
Last updated Mar 06, 2015, 8:37 PM
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A statistical technique to determine the line of best fit for a model. The least squares method is specified by an equation with certain parameters to observed data. This method is extensively used in regression analysis and estimation.
In the most common application - linear or ordinary least squares - a straight line is sought to be fitted through a number of points to minimize the sum of the squares of the distances (hence the name "least squares") from the points to this line of best fit.
In contrast to a linear problem, a non-linear least squares problem has no closed solution and is generally solved by iteration. The earliest description of the least squares method was by Carl Freidrich Gauss in 1795.
· Comment on Mar 07, 2015, 2:57 PM
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posted by DELILAH HENDERSON at Mar 07, 2015, 2:57 PM
Last updated Mar 07, 2015, 2:57 PM
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Thanks, Ariel, for your post. I looked up some more information on the least square approach and found an article "Least Squared Method' that explained it a little bit more. The article said "A statistical technique to determine the line of best fit for a model. The least squares method is specified by an equation with certain parameters to observed data. This method is extensively used in regression analysis and estimation." The article also gave a little more information, "In the most common application - linear or ordinary least squares - a straight line is sought to be fitted through a number of points to minimize the sum of the squares of the distances (hence the name "least squares") from the points to this line of best fit. In contrast to a linear problem, a non-linear least squares problem has no closed solution and is generally solved by iteration. The earliest description of the least squares method was by Carl Freidrich Gauss in 1795."
Reference:
http://www.investopedia.com/terms/l/least-squares-method.asp
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Linear Regression for Marketing The thread has 4 unread messages.
created by ERIK SEIDEL
Last updated Mar 07, 2015, 5:34 PM
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· Comment on Mar 06, 2015, 6:34 AM
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posted by ERIK SEIDEL at Mar 06, 2015, 6:34 AM
Last updated Mar 06, 2015, 6:34 AM
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Due to many changes and financial pressures in the health insurance industry, our company (and I'm sure others as well) are taking a harder look at administrative expenses and determining where budgets can be reduced. Without being administratively efficient, companies will go out of business. We're seeing more and more consolidations of health care organizations because of this. One area our company has focused on recently is marketing. It is often very difficult to determine the impact of increased or decreased advertising spending on new sales and retention. A linear regression model may help with this. If you have a few years of historical data, you can use marketing spending as the x variable and new sales as the y variable. You could do a similar analysis with marketing spending again as the x variable and retention of current customers as the y variable.
· Comment on Mar 07, 2015, 3:03 PM
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posted by DELILAH HENDERSON at Mar 07, 2015, 3:03 PM
Last updated Mar 07, 2015, 3:03 PM
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Erik, that is a good example. I was trying to apply linear regression where I work since I work at a university. I think we have the same relationship as your example, health insurance industry. I was thinking that instead of using marketing vs retention of current customers, in our example it could be variety of classes offered vs student enrollment. In our industry the type of classes or degrees offered would have a direct relation to student enrollment. I know we have studied this in depth because the type of classes offered and degrees has changed over the year based on student enrollment in these classes. One definitely affects the other.
d
· Comment on Mar 07, 2015, 5:34 PM
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posted by LOUIS DAILY at Mar 07, 2015, 5:34 PM
Last updated Mar 07, 2015, 5:34 PM
Delilah,
What university do you work for?
thanks
Lou
· Comment on Mar 07, 2015, 5:33 PM
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posted by LOUIS DAILY at Mar 07, 2015, 5:33 PM
Last updated Mar 07, 2015, 5:33 PM
Erik,
Sure. Good example of time series analysis in business.
thanks
Lou
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Sales Price and Linear Regression The thread has 5 unread messages.
created by ERIK SEIDEL
Last updated Mar 07, 2015, 2:54 PM
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· Comment on Mar 05, 2015, 5:06 AM
Message collapsed. Message unread Sales Price and Linear Regression
posted by ERIK SEIDEL at Mar 05, 2015, 5:06 AM
Last updated Mar 05, 2015, 5:06 AM
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As I think about linear regression further, I understand more and more how many applications it can have. Linear regression models can be a great tool for any company's sales department. For sales, linear regression can be used in tandem with a break-even analysis to determine the appropriate price to charge for a product. If a company gradually changes the price for a product but the linear regression line is flat or even sloping slightly upward, this means that people are continuing to purchase the product regardless of the price increase. On the other hand, if the slope is moving downward, the company may need to pull back on its price increases. This can help a company determine just how much it may be able to increase its product prices without losing sales volume and market share.
· Comment on Mar 05, 2015, 8:44 AM
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posted by CRYSTAL RAMOS at Mar 05, 2015, 8:44 AM
Last updated Mar 05, 2015, 8:44 AM
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In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variable) denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression.[1] (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.)[2]
In linear regression, data are modeled using linear predictor functions, and unknown model parameters are estimated from the data. Such models are called linear models.[3] Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X. Less commonly, linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X, which is the domain of multivariate analysis.
· Comment on Mar 05, 2015, 9:19 PM
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posted by ARACHEAL VENTRESS at Mar 05, 2015, 9:19 PM
Last updated Mar 05, 2015, 9:19 PM
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Thanks Erik for your example of how linear regression is used by businesses such as the retail industry when making strategic moves. I conducted more research about linear regression and business and found that linear regression can also be used to analyze risk
The example that I found discussed health insurance companies might conduct a linear regression plotting number of claims per customer against age and discover that older customers tend to make more health insurance claims. The results of such an analysis might guide important business decisions made to account for risk.
Reference
http://smallbusiness.chron.com/ways-linear-regression-
· Comment on Mar 07, 2015, 9:11 AM
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posted by Pierre at Mar 07, 2015, 9:11 AM
Last updated Mar 07, 2015, 9:11 AM
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Great post Erik,
Linear regressions are useful tools when it comes to predicting sales and the future growth of sales by analyzing the independent and dependent variable that effect the regression. There are two types of linear regressions. A simple regression is a regression that has only one independent variable present, and the second type of regression is a multiple regression when there are two or more independent variables used. The use of multiple independent variables in a regression is a more complicated relationship between the independent variables and the dependent variable in the multiple regression than the relationship between the two variables in a simple regression. According to the Columbia University Business school, "the most basic type of regression is that of simple linear regression. A simple linear regression uses only one independent variable, and it describes the relationship between the independent variable and dependent variable as a straight line."
Reference:
Statistical Sampling and Regression: Simple Linear Regression. (n.d.). Retrieved March 7, 2015, from https://www0.gsb.columbia.edu/premba/analytical/s7/s7_6.cfm
· Comment on Mar 07, 2015, 2:54 PM
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posted by DELILAH HENDERSON at Mar 07, 2015, 2:54 PM
Last updated Mar 07, 2015, 2:54 PM
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Thanks, Erik. That was a good post. I found an article, Introduction to Linear Regression, that said that "In simple linear regression, we predict scores on one variable from the scores on a second variable. The variable we are predicting is called the criterion variableand is referred to as Y. The variable we are basing our predictions on is called thepredictor variable and is referred to as X. When there is only one predictor variable, the prediction method is called simple regression. In simple linear regression, the topic of this section, the predictions of Y when plotted as a function of X form a straight line."
I believe this is what you were stating in your example on sales. That one variable can affect a second variable.The article also mentioned that "Linear regression consists of finding the best-fitting straight line through the points. The best-fitting line is called a regression line."
Reference:
http://onlinestatbook.com/2/regression/intro.html
