Question

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 + ?1?1 + ?2?2

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: 0.9994       Adjusted R-squared: 0.9994
F-statistic: 4.16e04 on 2 and 47 DF    p-value: < 2.2e-16

1. By using the above table, show how do we obtain the t-value for each coefficients.
2. Shall we remove the factor cost and/or rent based on its significance and why?
3. Which p-value corresponding to the testing of the overall significance of the model, and is it significance?

Answer 1

a)

t value for Intercept = 176.27867/ 23.36940 = 7.543

t value for rent = 0.55701/ 0.07114 = 7.830

t value for cost = 0.35332/ 0.10118 = 3.492

b)

For Rent:

As p-value < 0.05, we reject the null hypothesis.

It is significant. We will not remove rent.

For cost:

As p-value < 0.05, we reject the null hypothesis.

It is significant. We will not remove cost.

c)

P-value for overall model = 2.2e-16

As p-value < 0.05, we reject the null hypothesis.

The overall model is significant.