Question

# The real estate profession is interested in understanding how the rent (??1) and the cost to...

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?

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.

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