Question 10 (9 marks) Show the calculation step by step

The real estate profession is interested in understanding how the rent (1) and the cost to hold a one-bedroom apartment (2) affect the price of the one-bedroom apartment (y). He fits the model as:

= 0+ 11+ 22

Coefficients:

Estimate Std. Error t value Pr ( >|t|)

(Intercept) 176.27867 23.36940 7.543 <1.23e-9 ***

rent 0.55701 0.07114 7.830 <4.58e-10 ***

cost 0.35332 0.10118 3.492 < 0.00105 ***

Signif. codes:0 '***'0 '**'0.01'*'0.05 '.'0.1 ' '1

Residual standard error: 2.559 on 47 degrees of freedom

Multiple R-squared: 0.9994Adjusted R-squared: 0.9994

F-statistic: 4.16e04 on 2 and 47 DFp-value: < 2.2e-16

a)(3 marks) By using the above table, show how do we obtain the t-value for each coefficients.

b)(4 marks) Shall we remove the factor cost and/or rent based on its significance and why?

c)(2 marks) Which p-value corresponding to the testing of the overall significance of the model, and is it significance?