Question

The following exercise require a computer and software.

Calculate the coefficients of correlation for each pair of independent variables in Exercise. What do these statistics tell you about the independent variables and the t-tests of the coefficients?

Exercise

The following exercises require the use of a computer and statistical software. Exercises below can be solved manually.

A developer who specializes in summer cottage properties is considering purchasing a large tract of land adjoining a lake. The current owner of the tract has already subdivided the land into separate building lots and has prepared the lots by removing some of the trees. The developer wants to forecast the value of each lot. From previous experience, she knows that the most important factors affecting the price of a lot are size, number of mature trees, and distance to the lake. From a nearby area, she gathers the relevant data for 60 recently sold lots.

a. Find the regression equation.

b. What is the standard error of estimate? Interpret its value.

c. What is the coefficient of determination? What does this statistic tell you?

d. What is the coefficient of determination, adjusted for degrees of freedom? Why does this value differ from the coefficient of determination? What does this tell you about the model?

e. Test the validity of the model. What does the p-value of the test statistic tell you?

f. Interpret each of the coefficients.

g. Test to determine whether each of the independent variables is linearly related to the price of the lot in this model.

h. Predict with 90% confidence the selling price of a 40,000-square-foot lot that has 50 mature trees and is 25 feet from the lake.

i. Estimate with 90% confidence the average selling price of 50,000-square-foot lots that have 10 mature trees and are 75 feet from the lake.

Answer 1

The information is that the most important factors affecting the price of a lot prize, number of mature trees, and distance to the lake, from the nearby area of the 60 recently sold plots

From the above information the developer forecast the value of the each lot.

Let us consider the price of the lot is dependent variable and lot size, number of mature trees and distance to the lake are treated as independent variables.

We have to determine the coefficient of correlation between the each pair of independent variables.

Now compute the required correlation analysis using MINITAB by following the instructions:

1. Type or import the data into two adjacent columns.

2. Click Stat, Basic statistics, and Correlation.

3. Type the names of the variables in the Variables box.

4. Then click OK.

Performing the above instructions with the given data in MINITAB we can obtain the output of results as shown below:

From the above output we can say that there is correlation exists in between each pair

The regression output is,

Test of

From the regression output,

1) The null and alternative hypotheses are,

2) The level of the significance,

3) The test statistic is,

4) The P-value is 0.216

5) Here we observe that the P-value is greater than the given level of significance 0.05, so we fail to reject the null hypothesis. Therefore we conclude that the inclusion of the linear predictor is not important in the regression model.

Test of

From the regression output,

1) The null and alternative hypotheses are,

2) The level of the significance,

3) The test statistic is,

4) The P-value is 0.004

5) Here we observe that the P-value is less than the given level of significance 0.05, so we reject the null hypothesis. Therefore we conclude that the inclusion of the linear predictor is important in the regression model.

Test of

From the regression output,

1) The null and alternative hypotheses are,

2) The level of the significance,

3) The test statistic is,

4) The P-value is 0.058

5) Here we observe that the P-value is greater than the given level of significance 0.05, so we fail to reject the null hypothesis. Therefore we conclude that the inclusion of the linear predictor is not important in the regression model.