MAT305-Statistics-02, UG Spring 2017, Session 1 Eva Smith 3/2/17 6:33 PM Test: T
ID: 3173476 • Letter: M
Question
MAT305-Statistics-02, UG Spring 2017, Session 1 Eva Smith 3/2/17 6:33 PM Test: Test 4 (Ch 9 & 12) Submit Test This Question: 1 pt This Test: 10 pts possible 2 of 10 (1 complete) An agent for a real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of the apartment, as defined by square footage. A sample of eight apartments in a neighborhood was selected, and the information gathered revealed the data shown below. For these data, the regression coefficients are bo 142.7755 and b 1.0470. Complete parts (a) through (d). 925 1,825 1,250 Monthly Rent (S) 975 1,600 8000 1,450 1,950 Size (Square Fee) 800 1,200 950 1,150 1,900 750 1,350 1,100 a. Determine the coefficient of determination, and interpret its meaning. (Round to four decimal places as needed.) What is the meaning of r O A. measures the proportion of variation in monthly rent that can be explained by the variation in apartment sze. O B. r measures the proportion of variation in apartment size that cannot be explained by the variation in monthly rent. O C. measures the proportion of variation in monthly rent that cannot be explained by the variation in apartment size. O D. r measures the proportion of variation in apartment size that can be explained by the variation in monthly rent. b. Deter ne the standard error of the estima Syx, and interpret ts meaning ate, SYx Round to four decimal places as needed. What is the meaning of SYx? O A. SYx measures the amount by which an apartment's rent is greater than the rent predicted by the regression equation. O B. SYx measures the typical difference between an apartment s actual rent and the rent predicted by the regression equation. Click to select your answer(s).Explanation / Answer
Result:
Regression Analysis
r²
0.7893
n
8
r
0.8884
k
1
Std. Error
213.0097
Dep. Var.
rent
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,019,558.1317
1
1,019,558.1317
22.47
.0032
Residual
272,238.7433
6
45,373.1239
Total
1,291,796.8750
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=6)
p-value
95% lower
95% upper
Intercept
142.7755
264.9418
0.539
.6094
-505.5138
791.0648
size
1.0470
0.2209
4.740
.0032
a). R square= 0.7893
A. r2 measures the proportion of variation in monthly rent that can be explained by the variation in apartment size.
b). syx=213.0097
B. syx measures the typical difference between an apartment actual rent and the rent predicted by the model.
c). D. it is useful for predicting the monthly rent because r2 is close to 1 and syx is fairly small compared to the actual rents.
d).
select all the variables ( A,B,C,D,E)
Regression Analysis
r²
0.7893
n
8
r
0.8884
k
1
Std. Error
213.0097
Dep. Var.
rent
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,019,558.1317
1
1,019,558.1317
22.47
.0032
Residual
272,238.7433
6
45,373.1239
Total
1,291,796.8750
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=6)
p-value
95% lower
95% upper
Intercept
142.7755
264.9418
0.539
.6094
-505.5138
791.0648
size
1.0470
0.2209
4.740
.0032
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