Question

COMPUTER CALCULATIONS:

I need to know how to code in R for the solutions, not by hand.

2. Look at the data in Table 7.18 on page 368 of the textbook. These data are also

given in the SAS code labeled “SAS_basketball_goal_data” and R code labeled basketball goal data .

The dependent variable is goals and the independent variable is height of basketball players.

Complete a SAS /R program and answer the following questions about the data set:

(a) Does a scatter plot indicate a linear relationship between the two variables?

Is there anything disconcerting about the scatter plot? Explain.

(b) Fit the least-squares regression line (using SAS / R) and interpret the estimated slope

in the context of this data set. Does it make sense to interpret the estimated intercept? Explain.

(c) For these data, what is the unbiased estimate of the error variance? (Give a number.)

(d) Using the SAS / R output, test the hypothesis that the true slope of the regression line

is zero (as opposed to nonzero). State the appropriate null and alternative hypotheses,

give the value of the test statistic and give the appropriate P-value. (Use significance

level of 0.05.) Explain what this means in terms of the relationship between the two

variables.

(e) Using SAS / R, find a 95% confidence interval for the mean basketball goal for

a player with a height of 77 inches. In addition find a 95% prediction interval for

basketball goal for a player with a height of 77 inches.

Data:

Height	Goals
71	15
74	19
70	11
71	15
69	12
73	17
72	15
75	19
72	16
74	18
71	13
72	15
73	17
72	16
71	15
75	20
71	15
75	19
78	22
79	23
72	16
75	20
76	21
74	19
70	13

Answer 1

(a) Does a scatter plot indicate a linear relationship between the two variables?

Is there anything disconcerting about the scatter plot? Explain.

there is existence of linear relationship.

(b) Fit the least-squares regression line (using SAS / R) and interpret the estimated slope

in the context of this data set. Does it make sense to interpret the estimated intercept? Explain.

(Intercept) x  
-71.451 1.209  

there is 1.209 times effect on y in terms of x.

(c) For these data, what is the unbiased estimate of the error variance? (Give a number.)

MSE=0.6463807

(d) Using the SAS / R output, test the hypothesis that the true slope of the regression line

is zero (as opposed to nonzero). State the appropriate null and alternative hypotheses,

give the value of the test statistic and give the appropriate P-value. (Use significance

level of 0.05.) Explain what this means in terms of the relationship between the two

variables.

Estimate Std. Error t value Pr(>|t|)   
(Intercept) -71.45054 4.82700 -14.8 3.02e-13 ***
x 1.20946 0.06609 18.3 3.32e-15 ***

# R code for this problem is

data=read.csv("Book1.csv")
y=data$Goals
x=data$Height

plot(x,y,main = "plot of basketball goal data ")
fit=lm(y~x)
fit

# MSE
deviance(fit)/df.residual(fit)

#summary of fit
summary(fit)