Data analysis - Must be knowledeble in ststistics

Question 1 (2 points) 

In choosing the "best-fitting" line through a set of points in linear regression, we choose the one with the:

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In linear regression, a dummy variable is used:

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A multiple regression analysis included 4 independent variables results in sum of squares for regression of 1400 and sum of squares for error of 600. The multiple coefficient of determination will be:

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A "fan" shape in a scatterplot indicates:

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In regression analysis, the variables used to help explain or predict the response variable are called the

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A scatterplot that appears as a shapeless mass of data points indicates:

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The coefficient of determination () can be interpreted as the fraction (or percent) of variation of the

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The correlation value ranges from

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To help explain or predict the response variable in every regression study, we use one or more explanatory variables. These variables are also called predictor variables or independent variables.

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When the scatterplot appears as a shapeless swarm of points, this can indicate that there is no relationship between the response variable Y and the explanatory variable X, at least none worth pursuing.

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A useful graph in almost any regression analysis is a scatterplot of residuals (on the vertical axis) versus fitted values (on the horizontal axis), where a "good" fit not only has small residuals, but it has residuals scattered randomly around zero with no apparent pattern.

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A negative relationship between an explanatory variable X and a response variable Y means that as X increases, Y decreases, and vice versa.

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A regression analysis between weight (Y in pounds) and height (X in inches) resulted in the following least squares line: = 140 + 5X. This implies that if the height is increased by 1 inch, the weight is expected to increase on average by 5 pounds.

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In regression analysis, if the coefficient of determination is 1.0, then the coefficient of correlation must be 1.0.

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The residual is defined as the difference between the actual and fitted values of the response variable.

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If the coefficient of correlation is -0.88, then the percentage of the variation in Y that is explained by the regression is 77.44%.

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The coefficient of determination R2 is the square of the coefficient of correlation.

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A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: = 32 + 8X. This implies that an increase of $1 in advertising is expected to result in an increase of $40 in sales. BE CAREFUL!

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A multiple regression model has the form . The coefficient b1 is interpreted as the change in Y per unit change in X1.

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This question and the next two are based on the following information:   The maker of the Super B softball bat is interested in determining how certain factors affect the sales of its new model bat. The data below compares the number of bats (Y) that were sold, the average selling price (), and the disposable income per household () in the surrounding area at 10 large sporting goods stores that carry the Super B bat. Simple regression was used to compare each independent variable to the number of bats sold. The regression output from Excel is shown below:       Is there evidence of a linear relationship between the number of bats sold and the average selling price of the bats? Support your response. If you believe there is a linear relationship, characterize the relationship (i.e., positive, negative, strong, weak, etc.).

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Is there evidence of a linear relationship between the number of bats sold and disposable income in the area? Support your response If you believe there is a linear relationship, characterize the relationship (i.e., positive, negative, strong, weak, etc.).    

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Which of the two variables, the average selling price or the disposable income would you select for a simple linear regression model to predict the number of bats sold?

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This question and the next seven are based on the following information:   The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results:     Below is a scatterplot for this data. Comment on the relationship between shelf space and weekly sales.        

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Use StatTools to obtain the indicated simple linear regression results for the data given in Question 27. The output (with blank cells A-E) is given below.   Provide the correct values for cells A, B, C, D, and E.  

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What is the least squares estimate of the Y-intercept?

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What is the least squares estimate of the slope?

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Interpret the meaning of the slope b.

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Predict the average weekly sales (in hundreds of dollars) of international food for stores with 13 feet of shelf space for international food.

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Would it be appropriate to predict the average weekly sales (in hundreds of dollars) of international food for stores with 35 feet of shelf space for international food? Why or why not?

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State the value of the coefficient of determination, R2, and interpret its meaning.

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