Question

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
148	145
176	148
154	133
189	156
181	166
217	174
210	168
150	139
137	109
151	119
172	138
219	167
142	131
143	119
164	151
136	124
147	149
129	134
219	162
169	140
180	149
187	156
198	149
156	131
220	149
154	138
212	147
122	122
163	133
136	136

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.  

Answer 1

Answer:

We can solve it by using R software. First import the given data set into R.

R-code for confidence and prediction interval:

attach(data); #Attach given data set.
x = `Body weight`; # Denote independent variable Body weight = x.
y = `Bench press`; # Denote dependent variable Bench press = y.
reg_model = lm(y ~ x); # For generating simple linear regression model.
reg_model;
newdata = data.frame(x = 150); #for attaching the new value of Body weight = 150. #We now apply the predict function and set the predictor variable in the newdata argument. We also set the interval type as "predict" or "confidence", and use the default 0.95 confidence level.
predict(reg_model, newdata, interval = "confidence" ); # For estimating confidence interval for average Bench press.
predict(reg_model, newdata, interval = "predict"); # For estimating prediction interval for average Bench press.

Then from the R output:

reg_model:

Call:
lm(formula = y ~ x)

Coefficients:

Intercept	x
70.1712	0.4284

Confidence Interval:

Fit	Lower	Upper
134.436	130.0678	138.8042

Prediction Interval:

Fit	Lower	Upper
134.436	113.9732	154.8989

Ans (b):

Lower limit of confidence interval = 130.07

Ans (c):

Upper limit of confidence interval = 138.80

Ans (d):

Lower limit of prediction interval = 113.97

Ans (e):

Upper limit of prediction interval = 154.90