Question

4.-Interpret the following regression model
Call:
lm(formula = log(Sale.Price) ~ Lot.Size + Square.Feet + Num.Baths + 
    dis_coast + API.2011 + dis_fwy + dis_down + Pool, data = Training)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.17695 -0.23519 -0.00112  0.26471  1.02810 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  9.630e+00  2.017e-01  47.756  < 2e-16 ***
Lot.Size    -2.107e-06  3.161e-07  -6.666 4.78e-11 ***
Square.Feet  2.026e-04  3.021e-05   6.705 3.71e-11 ***
Num.Baths    6.406e-02  2.629e-02   2.437 0.015031 *  
dis_coast   -1.827e-05  6.881e-06  -2.655 0.008077 ** 
API.2011     3.459e-03  2.356e-04  14.680  < 2e-16 ***
dis_fwy      3.826e-06  8.140e-06   0.470 0.638452    
dis_down     1.176e-05  7.629e-06   1.541 0.123607    
Pool         2.046e-01  5.473e-02   3.738 0.000198 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3851 on 833 degrees of freedom
Multiple R-squared:  0.4808,    Adjusted R-squared:  0.4758 
F-statistic: 96.41 on 8 and 833 DF,  p-value: < 2.2e-16

Answer 1

From the given regression output above,

We want to test the hypothesis,

H0: The model is insignificant ( Null Hypothesis)

H1: The model is significant (Alternative Hypothesis)

Here , F=96.41

P value=0.0000000022

Here, P value is less than 0.05. We reject the null hypothesis at 5% level of significance

There is sufficient evidence to support the claim that the model is significant.

*** The independent variables like lot size, square feet, num bath , dis coast, API 2011, pool are significant because p value is less than 0.05.

*** Other variables are insignificant.