In a recent college statistics class, data was collected on each student\'s heig
ID: 3314757 • Letter: I
Question
In a recent college statistics class, data was collected on each student's height and their shoe size. The first three tables of the regression output are below the conclusions. Please agree or disagree with the conclusions and, of course, state your statistical reasoning.
1. There is sufficient statistical evidence of a strong, positive correlation between a student's height and shoe size.
2. About 65% of the variation in a student's shoe size is related to the variation in the student's height.
3. The relationship between student's shoe size and student's height is statistically significant because the "Intercept” tSTAT is less than the tSTAT for height.
Regression Statistics
R
0.80638
R-Squared
0.65025
Adjusted R-Squared
0.63897
S
1.19
Sample Size
33
Regression equation: shoe size = - 15.08781 + (0.35978 * Height)
ANOVA
d.f.
SS
MS
F
p-value
Regression
1.
81.61618
81.61618
57.63463
0
Residual
31.
43.89898
1.4161
Total
32.
125.51515
Coefficient
Standard Error
LCL
UCL
t Stat
p-value
Intercept
-15.08781
3.19558
-21.60524
-8.57038
-4.72146
0.00005
Height
0.35978
0.04739
0.26313
0.45644
7.59175
0
Tcrit (5%)
2.03951
Regression Statistics
R
0.80638
R-Squared
0.65025
Adjusted R-Squared
0.63897
S
1.19
Sample Size
33
Regression equation: shoe size = - 15.08781 + (0.35978 * Height)
ANOVA
d.f.
SS
MS
F
p-value
Regression
1.
81.61618
81.61618
57.63463
0
Residual
31.
43.89898
1.4161
Total
32.
125.51515
Coefficient
Standard Error
LCL
UCL
t Stat
p-value
Intercept
-15.08781
3.19558
-21.60524
-8.57038
-4.72146
0.00005
Height
0.35978
0.04739
0.26313
0.45644
7.59175
0
Tcrit (5%)
2.03951
Explanation / Answer
Ans:
1)test statistic
t=r*sqrt((n-2)/(1-r2))
t=0.806*sqrt((33-2)/(1-0.650))=7.585
df=33-2=31
p-value=0
As,p-value<0.0001,we reject null hypothesis.
There is sufficient statistical evidence of a strong, positive correlation between a student's height and shoe size.
2)Cofficient of determination,R2=SSR/SST=81.61618/125.51515=0.6502
65.02%
About 65% of the variation in a student's shoe size is related to the variation in the student's height.
So,option 2 is correct.
3)
t=0.35978/0.04739=7.592 (t stat for slope)
p-value=0
or t>2.039
So,we reject null hypothesis.
(we conclude significant relationship using t statistc for slope,not intercept)
The relationship between student's shoe size and student's height is statistically significant because the "Intercept” tSTAT is less than the tSTAT for height.(incorrect)
So, statement 1 and 2 are correct,and 3 is incorrect.
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