Module 6 Discussion-Stats

Running head: MODULE 6 DISCUSSION 1

MODULE 6 DISCUSSION 2

Module 6 Discussion

Student’s name

Professor’s name

Course title

Date

250 words Initial Post. will send replies later.

1. Describe an example of a research question where a Regression Model  could be been used. Describe the characteristics of the independent variables and their likelihood of explaining the variance in the dependent variable .  Discuss your estimate what you would expect the correlation coefficient to be between the pairs of each independent variable and the dependent variable.

A company that runs call centers can use regression analysis to determine the effect of decline in calls on sales. After understanding it, the company predicts how to solve the problem or figure out if this pattern will continue in the future. Generally, the sales tend to go down when the number of calls decline and vice versa. This reflects a positive relationship among the variables. Thus, they are strongly correlated to each other. Regression helps identify the strengths as well as the weaknesses in order to improve on them and push the calls drops upwards to increase sales. In this scenario, the independent variable is the calls whiles sales is the dependent variable. The regression equation can be stated as: y=bx+a where y is the dependent variable, x is independent variable, and “a” refers to the constant or y intercept. The values of x can be changed from time to time to find out what happens to y. Hence, independent variables are the variables which are manipulated. In addition, its impacts can be measured besides compared. They are also referred to as predictors because they forecast the dependent variable values. Dependent variables measure the effect of independent variable on test units. They depend on independent variables. They are the variables that are predicted. To be precise, regression is a method for relating the variables to one another (Black, 2017). The researcher observes the data, graphs it, and establishes if there is a pattern. Next, an equation is created that best matches the pattern. Deriving line of best fit is the most common form of linear regression.

2. Discuss how r^2 is valuable in determining the effectiveness of the regression model.

In your two replies to classmates, provide insights for the similarities and dissimilarities between their example and yours.

R2 or coefficient of determination analyzes strength of linear relationship among variables. It ranges between 0 and 1.0. 1.0 is a perfect fit and is most reliable for forecasting the future. 0 value shows that the model does not express the data accurately. R2 (0.60) reveals that 60% of the variation in dependent variable is explained by independent variable. A higher R2 means that the model can be strongly predicted. It indicates smaller variations between fitted values and observed data. After designing the linear model, the researcher wants to know how well the regression model matches with the data (Frost, 2020). R2 is one way of determining fitness. Goodness of fit examines the distance between the data points which are scattered in the diagram and the drawn line. Tight dataset will have a line which is close to the points and a high fitting level, a reflection that distance between the data and line is small. Notably, regression model best aligns with the data if the variations between observations and predicted values are small and not biased. Before evaluating the goodness of fit measures such as R2, assess residual plots. These plots show a biased model instead of numeric output. It indicates the patterns that have issues in residuals. The results are untrustworthy if he model is biased. If the residual plots are good then, proceed on to come up with r2. Adjusted R2 is recommended when analyzing the models fitness (Black, 2017). This adjusted model portrays the number of independent variables as well as the sample size. It may decrease or increase when an independent variable is added or removed. A rise in Adjusted R2 shows that the model has really improved.

References

Black, K. (2017). Business Statistics: For Contemporary Decision Making, (9th Edition). Hoboken, N.J.: Wiley.

Frost, J. (2020). How to interpret R-squared in regression analysis. Retrieved from https://statisticsbyjim.com/regression/interpret-r-squared-regression/