After running a simple regression analysis on a file contain

After running a simple regression analysis on a file containing real estate data with observations of variables Price(dependent variable) and Size:

1) What are the values of beta coefficients?

2) What is the interpretation of the intercept?

3) What is the interpretation of the slope?

4) Compute the t statistic for the slope?

5) Compute a 90% confidence interval for the slope.

6) What is the p value for the slope? Comment on its meaning and the outcome of the respective test.

7) What is the degrees of freedom for total?

8) What is the F sample value? Comment on its meaning and the outcome of the respective test.

9) What is the coefficient of determination? Comment on its meaning.

10) What is sum of squared errors?

1 SUMMARY OUTPUT Rearession Statistics 4 Multiple R 5 R Square 6 Adjusted R Square 0.506070324 7 Standard Error 8 Observations 0.712057372 0.5070257 12623.28081 518 10 ANOVA Significance F 184566797281 84566797281 530.70770962.75894E-81 MS 12 Regression 13 Residual 14 Total 516 82223164669 159347218.4 517 1.6679E+11 16 17 Intercept 18 Size 19 Coefficients Standard Error t Stat 22938.73729 37.70784032 P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 3110.83126 7.373828849 6.64831E-1316827.28521 29050.18937 16827.28521 29050.18937 1.63683145 23.03709421 2.75894E-81 34.49216704 40.9235136 34.4921670440.9235136

Solution

Solution:

(1)Since B₀ is the intercept term and B₁ represents the slope we can see that the fitted line is:

B₀₌22938.73729,B₁ =37.70784032

(2)22938.73729

(3)37.70784032,slope is positive

If a line has a positive slope (i.e. m > 0 ), then y always increases when x increases and y always decreases when x decreases.

x is size and y is price in this case.

(4)23.03709421

(5)

How to Find the Confidence Interval for the Slope of a Regression Line

Previously, we described how to construct confidence intervals. The confidence interval for the slope uses the same general approach. Note, however, that the critical value is based on a t score with n - 2degrees of freedom.

What is the 99% confidence interval for the slope of the regression line?

(A) 0.25 to 0.85
(B) 0.02 to 1.08
(C) -0.08 to 1.18
(D) 0.20 to 1.30
(E) 0.30 to 1.40

Solution

The correct answer is (C). Use the following four-step approach to construct a confidence interval.

(6)p value=2.75894E-81

(7)517

(8)F=530.7077096(by Anova test- The test actually uses variances to help determine if the means are equal or not.)

The difference was statistically significant

(9)coeff of determination=R²=0.5070257

=50.70257%

it implies that 51% of the variability between the two variables have been accounted for and the remaining 49% of the variability is still unaccounted for.

(10)In analysis of variance (ANOVA), the total sum of squares helps express the total variation that can be attributed to various factors

The total sum of squares = regression sum of squares (SSR) + sum of squares of the residual error (SSE)

=84566797281+82223164669