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# Regression Analysis

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LINEAR REGRESSION AND CORRELATION
Please note ALL answers and explanation is to be done in EXCEL -no word documents.

Question 1: The Bardi Trucking Co. located in Cleveland Ohio, makes deliveries in the great Laes region, the southeast and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a ship must travel and the length of time, in days; it takes the shipment to arrive at its destination. To investigate, Mr. Bardi selected a random sample of 20 shipments made last month. Shipping distance is the independent variable, and shipping time is the dependent variable, the results are as follows:

Shipment

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

DISTANCE IN (MILES)

656
853
646
783
610
841
785
639
762
762
862
679
835
607
665
647
685
720
652
828

Shipping Time (days)
5
14
6
11
8
10
9
9
10
9
7
5
13
3
8
7
10
8
6
10
Ques A. Determine and interpret the coefficient of determination.
QuesB. What would be the estimated shipping time for a distance of 715 miles?

Ques. 2. A sample of 12 homes sold last week in St. Paul Minnesota, is selected. The results are shown below.

Home size Selling Price Home size Selling Price
(Thousands of sq. feet) (\$thousands) (Thousands of sq ft) (\$Thousands)
1.4 100 1.3 110
1.3 110 0.8 85
1.2 105 1.2 105
1.1 120 0.9 75
1.4 80 1.1 70
1.0 105 1.1 95

Ques A: Determine AND INTERPRET THE COEEFICIENT OF DETERMINATION.

Quesb: What would be the estimated selling price of a home that has 1.0 thousand square feet?

PS: Any tips/pointers you can give for how to go about interpreting the coeeficient etc when it comes to linear Regression & Correlation so it's easier for me to understand?say in pointer form? Thanks

https://brainmass.com/statistics/regression-analysis/regression-analysis-147707

#### Solution Summary

Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.

\$2.19

## 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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