Question

In: Statistics and Probability

An exercise science major wants to try to use body weight to predict how much someone...

An exercise science major wants to try to use body weight to predict how much someone can bench press. He collects the data shown below on 30 male students. Both quantities are measured in pounds.

Body Weight Bench Press
147 134
134 131
141 125
129 135
152 147
176 142
196 171
200 158
132 134
176 153
204 153
194 156
211 164
145 129
180 141
201 162
124 118
145 151
172 143
145 137
137 121
153 143
191 170
177 160
150 138
202 157
144 135
151 153
202 157
216 169

a) What type of association does there appear to be between these two variables?
Solved Answer: positive association

b) Compute a 95% confidence interval for the average bench press of 150 pound males. What is the lower limit? Give your answer to two decimal places.

c) Compute a 95% confidence interval for the average bench press of 150 pound males. What is the upper limit? Give your answer to two decimal places.

d) Compute a 95% prediction interval for the bench press of a 150 pound male. What is the lower limit? Give your answer to two decimal places.

e) Compute a 95% prediction interval for the bench press of a 150 pound male. What is the upper limit? Give your answer to two decimal places.

Please provide formulas used for the confidence intervals and prediction intervals and standard error. Thank you!

Solutions

Expert Solution

Body Weight, X Bench Press, Y XY X² Y²
147 134 19698 21609 17956
134 131 17554 17956 17161
141 125 17625 19881 15625
129 135 17415 16641 18225
152 147 22344 23104 21609
176 142 24992 30976 20164
196 171 33516 38416 29241
200 158 31600 40000 24964
132 134 17688 17424 17956
176 153 26928 30976 23409
204 153 31212 41616 23409
194 156 30264 37636 24336
211 164 34604 44521 26896
145 129 18705 21025 16641
180 141 25380 32400 19881
201 162 32562 40401 26244
124 118 14632 15376 13924
145 151 21895 21025 22801
172 143 24596 29584 20449
145 137 19865 21025 18769
137 121 16577 18769 14641
153 143 21879 23409 20449
191 170 32470 36481 28900
177 160 28320 31329 25600
150 138 20700 22500 19044
202 157 31714 40804 24649
144 135 19440 20736 18225
151 153 23103 22801 23409
202 157 31714 40804 24649
216 169 36504 46656 28561
Ʃx = Ʃy = Ʃxy = Ʃx² = Ʃy² =
5027 4387 745496 865881 647787
Sample size, n = 30
x̅ = Ʃx/n = 167.567
y̅ = Ʃy/n = 146.233
SSxx = Ʃx² - (Ʃx)²/n = 23523.4
SSyy = Ʃy² - (Ʃy)²/n = 6261.37
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 10381

a) There appear to be a positive association between these two variables.

b) Slope, b = SSxy/SSxx = 0.441307296

y-intercept, a = y̅ -b* x̅ = 72.28494079

Regression equation :   

ŷ = 72.2849 + 0.4413 x  

Predicted value of y at X = 150

ŷ = 72.2849 + 0.4413 * 150 = 138.481  

Sum of Square error, SSE = SSyy -SSxy²/SSxx = 1680.140918

Standard error, se = √(SSE/(n-2)) = 7.74629

Critical value, t_c = T.INV.2T(0.05, 28) = 2.0484      

95% Confidence interval :

c) 95% Confidence interval :

d) 95% prediction interval:

e) 95% prediction interval:

orchestra answered 1 year ago
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