Question

The company Hanna Properties specializes in custom-home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. Thirty-three properties were randomly selected and square footage, number of bedrooms, number of bathrooms, number of days on the market, and selling price (in thousands of dollars) were investigated. In this problem, you will perform a regression analysis for selling price in terms of the other four variables

The data is available as Properties.txt

SALe_PRICE   SQFT   BEDROOMS   BATHS   DAYS
715   5232   5   5   8
583   4316   4   5   140
484   4238   4   4   229
425   3600   4   4   386
418   4000   4   3   0
418   3730   5   4   260
407   3005   4   3   81
405   3800   4   3   52
385   4127   4   4   108
336   3800   4   3   108
330   3200   4   3   52
330   3319   4   3   66
330   3259   4   3   121
319   3200   4   3   103
314   3400   5   3   60
308   3000   4   3   266
308   3007   4   3   144
297   3041   4   3   74
292   3043   4   3   110
286   3406   4   3   10
285   2539   4   2   44
283   3013   4   3   58
282   3022   4   3   171
272   2792   4   3   274
270   3407   4   3   31
267   3275   4   3   361
266   2826   4   3   88
266   2820   4   3   88
266   2826   4   3   252
264   2610   4   3   48
258   2790   3   3   33
253   2400   4   2   57
249   2780   3   3   223

Need questions (g) through (i) to be done with the R program please, I really need help with the R coding aspect.

(g) Do the data provide sufficient evidence to conclude that, taken together, square footage, number of bedrooms, number of bathrooms, and number of days on the market are useful for predicting selling price? Perform the required hypothesis test at the 1% significance level.

(h) For all homes in the Equestrian Estates that have 3200 sq ft, 4 bedrooms, 3 bathrooms, and that remain on the market for 60 days,
(i) Obtain a point estimate for the mean selling price.
(ii) Obtain a 95% confidence interval for the mean selling price.
(iii) Determine the predicted selling price.
(iv) Determine a 95% prediction interval for the selling price.

(i) Apply backward elimination to get a new model involving fewer predictors? What features make the new model better than the old one?

Answer 1

(g) Do the data provide sufficient evidence to conclude that, taken together, square footage, number of bedrooms, number of bathrooms, and number of days on the market are useful for predicting selling price? Perform the required hypothesis test at the 1% significance level.

Ans:

The P-value from the above table is 0.000 and smaller than 0.01 level of significance. Hence, the data provide sufficient evidence to conclude that, taken together, square footage, number of bedrooms, number of bathrooms, and the number of days on the market are useful for predicting selling price.

(h) For all homes in the Equestrian Estates that have 3200 sq ft, 4 bedrooms, 3 bathrooms, and that remain on the market for 60 days,
(i) Obtain a point estimate for the mean selling price.

Ans: SALe_PRICE = - 232.51 + 0.0831 *3200 + 22.88 *4 + 68.19 *3 - 0.0985 *60= 323.65
(ii) Obtain a 95% confidence interval for the mean selling price.

Ans: (305.02, 342.28)
(iii) Determine the predicted selling price.

Ans: Ans: SALe_PRICE = - 232.51 + 0.0831 *3200 + 22.88 *4 + 68.19 *3 - 0.0985 *60= 323.65

(iv) Determine a 95% prediction interval for the selling price.

Ans: (232.90, 414.40)