Answer to Question #260954 in Statistics and Probability for bri

Question

Bluereef real estate agent wants to form a relationship between the prices of houses, how many bedrooms, House size in sq ft and Lot Size in sq ft. The data pertaining to 100 houses were processed using MINITAB and the following is an extract of the output obtained: The regression equation is 𝑃𝑟𝑖𝑐𝑒 = 𝛽 + 𝜙𝐵𝑒𝑑𝑟𝑜𝑜𝑚 + 𝛾𝐻𝑜𝑢𝑠𝑒 𝑆𝑖𝑧𝑒 + 𝜆𝐿𝑜𝑡 𝑆𝑖𝑧𝑒 Predictor Coef SE Coef T P Constant 37718 14177 2.66 ** Bedrooms 2306 6994 0.33 0.742 House Size 74.3 52.98 * 0.164 Lot Size -4.36 17.02 -0.26 0.798 S= 25023 R-Sq=56.0% R-Sq(adj)=54.6% Source DF SS MS F P Regression 3 76501718347 25500572782 *** **** Residual Error 96 60109046053 626135896 Total 99 a) Write out the regression equation. [1] b) Fill in the missing values *, **, *** and ****. [6]

Answer 1

a) The estimated regression equation is

b) * denotes the T value of house size.

$T =\frac{coef}{ SE \;coef} \\ T = \frac{74.3}{52.98} \\ T = 1.40$

Now, ** denotes the P- value of constant.

Here the df = n-4 = 100-4 = 96. The T value of constant is 2.66.

So, the P-value corresponding to 96 df and T=2.66 from the t distribution table is 0.009

P-value = 0.009

Now, *** denotes the F statistic value.

$F = \frac{MS_{reg}}{MS_{res}} \\ F = \frac{25500572782 }{ 626135896} \\ F = 40.73$

Now, **** denotes the P-value of the F statistic.

Here the P-value corresponding to (3,96) df from the F distribution table is approximately 0.

P-value = 0.000