Question

An agent for a real estate company wanted to predict the monthly rent for apartments based on the size of the apartment. The data for a sample of 25 apartments is available below. Perform a t test for the slope to determine if a significant linear relationship between the size and the rent exists. a. At the 0.05 level of​ significance, is there evidence of a linear relationship between the size of the apartment and the monthly​ rent? b. Construct a​ 95% confidence interval estimate of the population​ slope, beta1

A. Find the test statistic.

B. What is the​ p-value?

C.  The​ 95% confidence interval is

____less than or equals≤betaβ1less than or equals≤_______.Size_(sq._ft)   Rent_($)

840   1925
1440   2575
1085   2200
1242   2525
708   1925
1495   2700
1146   2675
716   1945
700   1875
966   2150
1100   2375
1295   2675
1995   3325
1379   2775
1165   2375
1215   2475
1235   2100
1269   2725
1160   2225
886   2125
1371   2625
1050   2625
745   2175
990   1800
1210   2775

Answer 1

applying regression on above data":

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1152.131088	155.7073372	7.39933717	1.59E-07	830.0259197	1474.236256	830.0259197	1474.236256
x	1.08674164	0.13286674	8.17918494	2.93E-08	0.811885847	1.361597433	0.811885847	1.361597433

a)

test statistic =8.179
b)

p-value =0.0000

c)

95% confidence interval estimate of the population​ slope =0.8119 < beta1 <1.3616