Question Question 1(2 points) In choosing the “best-fitting” line through a set of points in linear regression we choose the one with the: Question 2(2 points) In linear regression a dummy variable is used: Question 3(4 points) 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: Question 4(2 points) A “fan” shape in a scatterplot indicates: Question 5(2 points) In regression analysis the variables used to help explain or predict the response variable are called the Question 6(2 points) A scatterplot that appears as a shapeless mass of data points indicates: Question 7(2 points) The coefficient of determination () can be interpreted as the fraction (or percent) of variation of the Question 8(2 points) The correlation value ranges from Question 9(2 points) 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. Question 10(2 points) 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. Question 11(2 points) 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. Question 12(2 points) A negative relationship between an explanatory variable X and a response variable Y means that as X increases Y decreases and vice versa. Question 13(4 points) 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. Question 14(4 points) In regression analysis if the coefficient of determination is 1.0 then the coefficient of correlation must be 1.0. Question 15(4 points) The residual is defined as the difference between the actual and fitted values of the response variable. Question 16(4 points) 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%. Question 17(4 points) The coefficient of determination R 2 is the square of the coefficient of correlation. Question 18(4 points) 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! Question 19(2 points) A multiple regression model has the form.The coefficient b1is interpreted as the change in Y per unit change in X1. Question 20(4 points) This question and the next two are based on the following information: The maker of theSuper Bsoftball 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 theSuper Bbat. 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.). Question 21(4 points) Is there evidence of a linear relationship between the number of bats sold anddisposable 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.). Question 22(2 points) 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? Question 23(3 points) 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. Question 24(5 points) Use StatTools to obtain the indicated simple linear regression results for the data given in Question 23. The output (with blank cells A-E) is given below. Provide the correct values for cells A B C D and E. Question 25(2 points) What is the least squares estimate of theY-intercept? Question 26(2 points) What is the least squares estimate of theslope? Question 27(2 points) Interpret the meaning of the slopeb. Question 28(4 points) Predict the average weekly sales (in hundreds of dollars) of international food for stores with 13 feet of shelf space for international food. Question 29(4 points) 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? Question 30(4 points) State the value of the coefficient of determination R 2 and interpret its meaning.
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