Question

In: Statistics and Probability

An agent for a real estate company wanted to predict the monthly rent for apartments based...

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.

Size_(sq._ft)   Rent_($)
850   1925
1460   2600
1075   2200
1222   2475
708   1925
1495   2675
1146   2650
726   1925
710   1875
966   2125
1100   2375
1285   2650
1995   3325
1369   2775
1185   2400
1235   2425
1255   2075
1249   2725
1140   2175
896   2125
1351   2600
1050   2650
765   2175
1010   1800
1200   2750

a. Determine hypothesis

b. t stat = ?

c. p value =

d. reach a decision to reject or not and with sufficient or insufficient evidence

e. Develop 95% confidence interval

Solutions

Expert Solution

size rent
850 1925
1460 2600
1075 2200
1222 2475
708 1925
1495 2675
1146 2650
726 1925
710 1875
966 2125
1100 2375
1285 2650
1995 3325
1369 2775
1185 2400
1235 2425
1255 2075
1249 2725
1140 2175
896 2125
1351 2600
1050 2650
765 2175
1010 1800
1200 2750

EXCEL OUTPUT:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.849297387
R Square 0.721306052
Adjusted R Square 0.709188924
Standard Error 199.0735527
Observations 25
ANOVA
df SS MS F Significance F
Regression 1 2359103.574 2359103.574 59.5278058 7.93915E-08
Residual 23 911496.4256 39630.27938
Total 24 3270600
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1144.076975 164.5592794 6.952369861 4.36316E-07 803.6601689 1484.493781 803.6601689 1484.493781
SIZE 1.082799832 0.140342188 7.715426482 7.93915E-08 0.792479897 1.373119767 0.792479897 1.373119767

A) HO: β1=0

H1: β≠0 IS CORRECT.

B) t Stat value is 7.715426482

C) p-value is 0.0000000793915 ≈ 0

D) Here p-value is less than 0.05 so we reject the null hypothesis and also we have sufficient evidence that to conclude there is a relationship between monthly rent and apartment size.

E) The 95% C.I is 0.792479897480759 to 1.37311976723654

orchestra answered 3 years ago
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