- Obtain descriptive statistics, a boxplot, and histogram for Sales to help you analyze the TV unit sales for all 80 stores (as a single group). Summarize your most important findings to the manager.
- The national manager is wondering if having a special display seems to make any difference in TV unit sales. To address this question, sort the data using Display as the key variable then again obtain descriptive statistics (this time including 95% confidence intervals for the population mean), a boxplot, and histogram for Sales, for each type of Display. Does it seem that the display type makes a difference?
- The national manager would like to set a weekly target of 60 units sold for these TV units. Refer to your outputs from question #2. The distribution of TV unit sales in each sample is approximately mound-shaped. Assume that the normal distribution is applicable here, and that the sample mean and standard deviation are good estimates of the true population mean and standard deviation. Use these printouts to estimate (with an approximate probability) how likely it is that the actual TV unit sales will meet or exceed this target for each of the two display types. Based on your probabilities as well as confidence intervals for the mean Sales, with which display type does it appear that the target can be more easily met?
- Test the hypothesis, at the 5% significance level, that the mean number of TV units sold using a special store-front display exceeds that when no special display is used. State the hypotheses, the decision, and conclusion. Clearly explain the reason for arriving at your conclusion. Does your conclusion here agree with your findings in question #2? Explain.
- Obtain a 90% confidence interval for the difference in the mean number of TV units sold when a special store front display is used compared to when no special display is used. Relate this finding to your results in #4.
- Generate three separate simple regression models to investigate the individual effect, on the number of units sold, of price, number of TV ads per week, and display type. Use r-square values as well as confidence intervals or hypothesis tests on the regression slopes to assess the regression models and to shed light on how price, number of TV ads per week, and display type individually affect the number of units sold. Support your conclusion with scatter-plots of Y vs. X for each of the simple regressions.
- Conduct a multiple regression analysis of the relationship between the number of TV units sold (Sales) and the set of independent variables: Price, TV-Ads and Display. Explain your regression function to the national manager. Include in your explanation the meaning of the RSquare and Regression Standard Error statistics in the regression output. What additional information does your multiple regression model provide when compared to the three separate regression models in #6 above?
- To illustrate one use of regression, obtain a 95% interval for the predicted number of TV units sold, using the sample regression function for the following situations:
- Use your insights from 1-9 above to make a set of recommendations regarding the chain’s pricing and marketing policies.