The data show the list and selling prices for several expensive homes. Find the

Question

The data show the list and selling prices for several expensive homes. Find the regression equation, letting the the list price be the independent (x) variable. Find the best predicted selling price of a home having a list price of

$22

million. Is the result close to the actual selling price of

$2.22.2

million? Use a significance level of 0.05.

List price (millions of $)

1.61.6

4.24.2

2.12.1

1.61.6

2.32.3

44

  

Selling price (millions of $)

22

4.64.6

1.81.8

1.91.9

2.42.4

3.63.6

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Click the icon to view the critical values of the Pearson correlation coefficient r.

What is the regression equation?

ModifyingAbove y with caretyequals=nothingplus+nothingx

(Round to four decimal places as needed.)

List price (millions of $)

1.61.6

4.24.2

2.12.1

1.61.6

2.32.3

44

  

Selling price (millions of $)

22

4.64.6

1.81.8

1.91.9

2.42.4

3.63.6

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 0.28185798 + 0.92461089 x
Sample size: 6
R (correlation coefficient) = 0.95320474
R-sq = 0.90859928
Estimate of error standard deviation: 0.38385619

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

Regression equation:

y = 0.2819 + 0.9246 x

Predicted selling price for a list price of $2 million = $2.1 million

Yes, this result is close to actual selling price of $2.1 million.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 0.28185798 0.41670979 0 4 0.67638915 0.5359 Slope 0.92461089 0.14662824 0 4 6.3058173 0.0032

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