I have completed the first part of the question. The results are below. I need h

Question

I have completed the first part of the question. The results are below. I need help with the second part of the questions which is the following:

State the linear equation.

Explain the overall statistical significance of the model.

Explain the statistical significance for each independent variable in the model

Interpret the Adjusted R2.

Is this a good predictive equation(s)? Which variables should be excluded (if any) and why? Explain

Thank you!

Selling Price ($) Square Footage Bedrooms Age (Years) 84,000 1670 2 30 79,000 1339 2 25 91,500 1712 3 30 120,000 1840 3 40 127,500 2300 3 18 132,500 2234 3 30 145,000 2311 3 19 164,000 2377 3 7 155,000 2736 4 10 168,000 2500 3 1 172,500 2500 4 3 174,000 2479 3 3 175,000 2400 3 1 177,500 3124 4 0 184,000 2500 3 2 195,500 4062 4 10 195,000 2854 3 3 Linear Regression Regression Statistics R 0.93154 R-square 0.86777 Adjusted R-square 0.83726 S 15,231.90386 N 17 ANOVA d.f. SS MS F p-level Regression 3. 1.97945E+10 6,598,158,669.42469 28.439 5.55716E-6 Residual 13. 3,016,141,638.78474 232,010,895.29113 Total 16. 2.28106E+10 Coefficient Standard Error LCL UCL t Stat p-level H0 (5%) Intercept 91,446.49299 26,076.89048 35,110.79614 147,782.18984 3.5068 0.00386 rejected Square Footage 29.85788 10.8609 6.39434 53.32142 2.74912 0.01657 rejected Bedrooms 2,116.85543 10,003.00921 -19,493.33215 23,727.043 0.21162 0.83568 accepted Age -1,504.76587 370.82037 -2,305.87457 -703.65717 -4.05794 0.00136 rejected Selling Price = 91,446.49 + 29.86 x Square Footage + 2,116.86 x Bedrooms - 1,504.77 x Age Selling Price = 91,466.49 + 29.86(2,000) + 2,116.86(3) - 1,504.77(10) = $142,129.37 The predicted selling price for a house that is 1-0years-old, 3 bedrooms and 2,000 square feet is $142,129.37

Explanation / Answer

Assume alpha = level of significance = 5% = 0.05

Here the dependent variable (Y) is selling price and there are three independent variables.

Three independent variables are square footage(X1), bedrooms(x2) and age(X3).

State the linear equation.

The linear equation is,

Selling Price = 91,446.49 + 29.86 x Square Footage + 2,116.86 x Bedrooms - 1,504.77 x Age

Explain the overall statistical significance of the model.

This we can done by using ANOVA table.

The hypothesis for the test is,

H0 : B1 = B2 = B3 = 0

H1 : Atleast one of Bj is not 0. j = 1,2,3

And in the ANOVA output p-value for F-test is 5.55716E-6 which is approximately 0.000005557.

p-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of Bj is not 0.

Explain the statistical significance for each independent variable in the model.

Here the test of hypothesis is,

H0 : Bj = 0 Vs H1 : Bj 0 (for j=1,2,3)

There are three independent variables.

For variable square footage p-value is 0.01657 which is less than alpha.

Reject H0 at 5% level of significance.

Conclusion : Slope for square footage is differ than 0.

Similarly for variable bedrooms p-value is 0.83568 which is greator than alpha.

Accept H0 at 5% level of significance.

Conclusion : Slope for bedrooms is 0.

And for the third variable age p-value is 0.00136 which is less than alpha.

Reject H0 at 5% level of significance.

Conclusion : Slope for age is differ than 0.

Interpret the Adjusted R2.

Adjusted R2 indicates how well terms fit a curve or line, but adjusts for the number of terms in a model.

adjusted R2 = 0.83726 = 0.83726*100 = 83.73%

The adjusted R-squared compares the explanatory power of regression models that contain different numbers of predictors.

And for the third variable age p-value is 0.00136 which is less than alpha.

Reject H0 at 5% level of significance.

Conclusion : Slope for age is differ than 0.

Interpret the Adjusted R2.

Adjusted R2 indicates how well terms fit a curve or line, but adjusts for the number of terms in a model.

adjusted R2 = 0.83726 = 0.83726*100 = 83.73%

The adjusted R-squared compares the explanatory power of regression models that contain different numbers of predictors.

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