Let x be a random variable that represents the percentage of successful free thr
ID: 2946546 • Letter: L
Question
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x
87
88
70
84
78
76
y
53
57
50
51
46
50
Given that Se = 3.054, a= 16.547, b= 0.425, and , find the predicted percentage of successful field goals for a player with x= 73% successful free throws.
x
87
88
70
84
78
76
y
53
57
50
51
46
50
Explanation / Answer
In R find the regression model
Rcode is
x <- c(87,88,70,84,78,76)
y <- c(53,57,50,51,46,50)
rmod1 <- lm(y~x)
summary(rmod1)
output:
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5 6
-0.4121 3.2424 2.4606 -1.3758 -4.3030 0.3879
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 23.3576 15.6745 1.49 0.21
x 0.3455 0.1941 1.78 0.15
Residual standard error: 3.054 on 4 degrees of freedom
Multiple R-squared: 0.4419, Adjusted R-squared: 0.3024
F-statistic: 3.168 on 1 and 4 DF, p-value: 0.1497
y=23.3576+ 0.3455 *x
slope=0.3455
y intercept=23.3576
For x=73
we get
y=23.3576+ 0.3455 *73
y= 48.5791
y=49
rounding to nearest integer
the predicted percentage of successful field =49
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