The data on the file HW_04_Q_6 contains the heights and best bench-press weights
ID: 3052002 • Letter: T
Question
The data on the file HW_04_Q_6 contains the heights and best bench-press weights achieved by 48 weight lifters. Analyze data to determine whether or not you think there is a relationship between height and ability to lift weights (at least as measured by the bench press). Compute a linear regression line to fit this data, also compute the correlation coefficient and coefficient of determination. Answer the following questions:
A) how many more (or fewer) pounds does the typical weight lifter in this sample bench press for each increase of one inch of height. What is the name of the statistic you use to answer this question?
B) What is the predicted weight lifted by a person with a height of zero (0) inches. Why does this silly number (a person with no height) make sense? What is this statistic called?
C) What weight would a person with a height of 60 inches be predicted to lift?
D) What range of variation do you expect in this estimate? (Assume homoscadasticity). What is the name of the statistic you calculated to compute this error range.
E) What proportion of variation in weight lifting ability do you think might be accounted for by a person’s height? What is the name of the statistic that allows you to calculate this?
F) What other factors might account for the variation that cannot be accounted for by the relationship between height and weight lifting ability? How large is this amount?
Height Weight 55 60 55 90 55 130 55 200 55 280 55 110 55 50 55 270 55 90 55 170 55 230 55 240 55 220 55 120 55 140 55 180 55 80 56 70 57 280 58 170 58 90 59 170 59 220 59 170 59 170 59 150 59 160 59 40 59 210 59 90 59 300 59 70 59 240 59 270 60 220 60 230 60 150 60 210 60 280 60 80 60 160 61 150 61 160 61 270 61 240 61 310 61 90 61 180Explanation / Answer
Result:
A) how many more (or fewer) pounds does the typical weight lifter in this sample bench press for each increase of one inch of height. What is the name of the statistic you use to answer this question?
6.7081 more pounds, Regression coefficient or slope
B) What is the predicted weight lifted by a person with a height of zero (0) inches. Why does this silly number (a person with no height) make sense? What is this statistic called?
-216.1499, intercept or constant.
There is no meaning because it is negative.
C) What weight would a person with a height of 60 inches be predicted to lift?
Regression lie : weight = -216.1499+6.7081*height
Predicted weight = -216.1499+6.7081*60
=186.34 pounds
D) What range of variation do you expect in this estimate? (Assume homoscadasticity). What is the name of the statistic you calculated to compute this error range.
Standard error = 73.164
E) What proportion of variation in weight lifting ability do you think might be accounted for by a person’s height? What is the name of the statistic that allows you to calculate this?
R square or coefficient of determination = 0.046
F) What other factors might account for the variation that cannot be accounted for by the relationship between height and weight lifting ability? How large is this amount?
variation that cannot be accounted or coefficient of nondetermination =0.954
95.4% of variance not explained.
Regression Analysis
r²
0.046
n
48
r
0.213
k
1
Std. Error
73.164
Dep. Var.
Weight
ANOVA table
Source
SS
df
MS
F
p-value
Regression
11,756.0048
1
11,756.0048
2.20
.1452
Residual
246,235.6619
46
5,352.9492
Total
257,991.6667
47
Regression output
confidence interval
variables
coefficients
std. error
t (df=46)
p-value
95% lower
95% upper
Intercept
-216.1499
262.1875
-0.824
.4140
-743.9060
311.6061
Height
6.7081
4.5266
1.482
.1452
-2.4034
15.8196
Predicted values for: Weight
95% Confidence Interval
95% Prediction Interval
Height
Predicted
lower
upper
lower
upper
Leverage
60
186.338
157.585
215.091
36.286
336.390
0.038
Regression Analysis
r²
0.046
n
48
r
0.213
k
1
Std. Error
73.164
Dep. Var.
Weight
ANOVA table
Source
SS
df
MS
F
p-value
Regression
11,756.0048
1
11,756.0048
2.20
.1452
Residual
246,235.6619
46
5,352.9492
Total
257,991.6667
47
Regression output
confidence interval
variables
coefficients
std. error
t (df=46)
p-value
95% lower
95% upper
Intercept
-216.1499
262.1875
-0.824
.4140
-743.9060
311.6061
Height
6.7081
4.5266
1.482
.1452
-2.4034
15.8196
Predicted values for: Weight
95% Confidence Interval
95% Prediction Interval
Height
Predicted
lower
upper
lower
upper
Leverage
60
186.338
157.585
215.091
36.286
336.390
0.038
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