Linear Regression

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Linear-Regression Analysis
Introduction
Whitner Autoplex located in Raytown, Missouri, is one of the AutoUSA dealerships. Whitner Autoplex includes Pontiac, GMC, and Buick franchises as well as a BMW store. Using data found on the AutoUSA website, Team D will use Linear Regression Analysis to determine whether the purchase price of a vehicle purchased from Whitner Autoplex increases as the age of the consumer purchasing the vehicle increases. The data set provided information about the purchasing price of 80 domestic and imported automobiles at Whitner Autoplex as well as the age of the consumers purchasing the vehicles. Team D selected the first 30 of the sampled domestic vehicles to use for this test. The business research question Team D will answer is: Does the purchase price of a consumer increase as the age of the consumer increases? Team D will use a linear-regression analysis to test the age of the consumers and the prices of the vehicles. Five Step Hypothesis Testing

Team D will conduct the two-sample hypothesis using the following five steps: 1. Formulate the hypothesis
2. State the decision rule
3. Calculate the Test Statistic
4. Make the decision
5. Interpret the results
Step 1- Formulate the Hypothesis
Using the research question: Does the purchase price of an automobile purchased at Whitner Autoplex, increase as the age of the consumer purchasing the vehicle increases? The hypothesis in verbal terms would be: Ho: If β1 = 0, then X cannot influence Y and the regression model collapses to a constant β0 plus a random error. H1: If β1 is unequal to 0, then X can influence Y and the regression model will not collapse. The hypothesis stated in symbolic form is:

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Step 2 - State the Decision Rule

From the tables we find that the critical value at a 0.05 level of significance is 1.701. Team D will reject the null hypothesis if R² is less than the critical value of 1.701.

Step 3 - Calculate the Test Statistic

The data set that Team D has used is Whitner Autoplex, is shown on the next page and was taken from Statistical Techniques in Business & Economics, (Lind, Marchal, and Wathen, 2008): |Age |Price |

|25 |15935 |
|26 |15546 |
|28 |17357 |
|28 |20047 |
|29 |17399 |
|29 |18021 |
|30 |15794 |
|30 |17968 |
|31 |18890 |
|31 |24609 |
|32 |17266 |
|33 |17891 |
|33 |20155 |
|34 |20445 |
|35 |19331 |
|35 |19688 |
|35 |20642 |
|36 |20203 |
|37 |21639 |
|37 |27453 |
|38 |28034 |
|38 |28683 |
|39 |18263 |
|39 |20642 |
|40 |20454 |
|41 |21442 |
|41 |22442 |
|41 |22845 |
|42 |19251 |
|42 |26613 |
| | |

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The summary of data is as follows:

Y = 423.4x + 5890

R² = 0.359

Step 4: Make the Decision

From the tables we find at a 0.05 level of significance the critical value is 1.701. This value 0 falls within the “Reject Ho” area because 0.359 is less than the critical value of 1.701, therefore Team D rejects the null Hypothesis.

Step 5: Interpret the results

At a level of significance of 5% we are able to determine conclusively that purchase price of domestic vehicles purchased at Whitner Autoplex does increase for 36 percent of the sample (R² = 0.359), however for the remaining 64 percent, this is not the case and the age of the consumer has no perceptible affect on the purchase price...
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