.A retail store manager with Petrie Stores, Inc, wants to develop a multiple regression model to predict the amount of sales of a product per month Y from monthly advertising expenditures X1 and whether the month was December (coded 1) or another month (coded 0) X2. The multiple regression results are presented below. *will attach*
(a)Construct a scatterplot between sales (Y) and advertising expenditures (X1). See data to the right. Provide a standard evaluation of the scatterplot.
(b)Which of the explanatory variables (if any) are statistically significant (at the .05 level) in explaining product sales per month? Conduct a formal hypothesis test for each estimated regression coefficient.
(c)Give an interpretation (as applicable to the data) for each of the estimated regression coefficients.
(d)How much of the variation of y around ybar can be explained by the regression model?
(e)Conduct an F-Test (.05 level) to test for a globally statistically significant regression equation.
(f)Find the predicted sales per month when advertising expenditures equal $2,000 and the month is July.
(g)Find the predicted sales per month when advertising expenditures equal $2,000 and the month is December.
(h)Provide a brief evaluation of the estimated regression equation. Would the equation be suitable for forecasting?
2.A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year Y, and the distance (miles) X1 between home and work for the employees. A sample of 5 employees was chosen, and the following data were collected.
Distance to Work Number of Days Absent
(X1) (Y)
1 8
3 5
8 6
12 5
18 2
(a) Construct a scatterplot using Excel. Provide a standard evaluation of the scatterplot.
(b)Estimate the slope coefficient and intercept term for the regression line that relates number of absent days to distance to work by hand. Express the estimated equation in standard form.
(c) Interpret (as applicable to the data) the estimated slope coefficient and intercept term.
(d)Compute the Errors, Sum of Squared Errors (SSE), Mean Square Error (MSE) and Regression Standard Error (SE).
3.Based on the estimated regression equation in Question Two and the calculated SSE, MSE & SE, does a statistically significant (.05 level) relationship exist between the number of days absent and the distance to work? Hint: Perform a hypothesis test on the slope coefficient.