Question

Suppose the following data were collected relating the selling price of a house to square footage and whether or not the house is made out of wood. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average wood houses are more expensive than other types of houses at the 0.01 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."

Suppose the following data were collected relating the selling price of a house to square footage and whether or not the house is made out of wood. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average wood houses are more expensive than other types of houses at the 0.01 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence." Copy Data

Answer 1

We will perform regression analysis in R-Studio. We will check the following hypothesis:

Ho: Wood houses are not more expensive than other types of houses i.e Coefficient <= 0

Ha: The coefficient of wood is significantly greater than zero

Run the following code in R:

Price = c(202811,228434,196739,211351,156012,196376,157448,199109,230693,223887,192221,212126,222680,193288,186073,157059,192158,253527,167611,218069)
> Sqft=c(2402,3413,2414,2761,1718,2304,1425,2477,3320,3046,2353,2827,3067,2012,1832,1459,2165,3536,1411,2877)
> Wood = c(1,1,0,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,1,1)
> Model = lm(Price~Sqft+Wood)
> summary(Model)

The results are:

Call:
lm(formula = Price ~ Sqft + Wood)

Residuals:
     Min       1Q   Median       3Q      Max 
-13477.8  -1956.4     45.4   2249.0  13804.2 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.031e+05  5.799e+03  17.784 2.02e-12
Sqft        3.863e+01  2.232e+00  17.311 3.13e-12
Wood        4.930e+03  2.885e+03   1.709    0.106
               
(Intercept) ***
Sqft        ***
Wood           
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6451 on 17 degrees of freedom
Multiple R-squared:  0.9469,    Adjusted R-squared:  0.9407 
F-statistic: 151.7 on 2 and 17 DF,  p-value: 1.446e-11

We can see that the coefficient of wood has a p-value of 0.106 which means that it is not significant at 0.01 level of significance. Hence, we cannot reject the null hypothesis

Correct answer: Not enough evidence