# A problem on Regression analysis

ACCT 240

Pizza Project #1

This assignment requires the use of spreadsheet software to analyze cost data using regression analysis and scatter plot graphs. The data to be analyzed are printed on the next page. Your assignment is as follows:

1. Produce ten scatter plot graphs with the number of pizzas sold as the predictor variable. The scatter plot graphs for the nine expenses and total costs should show the actual data points.

2. Add a trend line, regression output, and R-square statistic for each scatter plot graph. (The number of pizzas is the independent variable (X) and the cost data is the dependent variable (Y).

3. Prepare a summary table by using selected data from the regression output: the constant (a), the X coefficient (b), and the R-square statistic for each cost item. A check row should be used to total the (a)s and the (b)s for the nine expenses. These totals should be equal to the regression output for the total expense line.

4. Time series scatter plot graphs for the cost items. (Several cost items could be combined on one graph).

5. The time series plots may reveal information about cost behavior patterns that are more useful for predictive purposes than the regression data based on volume. For each cost equations, please explain whether the regression equation or the time series graph is a better predictor of costs.

Grading Criteria (30 Points Total)

1. (12 pts.) Ten scatter plot graphs

2. (6 pts.) For each graph, provide a trend line, fixed cost, variable cost, and R-square statistic.

3. (6 pts.) Nine time series lines

4. (3 pts.) Summary table

5. (3 pts.) Explanation of how this information might be used to predict costs

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Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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