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Concept explainers
(a)
To find: The equation for the appropriate least-squares regression line.
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 6CRE
The equation of least-squares regression line isY=30.2+0.16X
Explanation of Solution
Given:
r = 0.6 ,
The Pre −exam:
mean 280 and standard deviation 30,
The final-exam:
mean 75 and standard deviation 8.
Calculation:
The slope of the least-square regression line of Final exam scores based on pre-exam scores is calculated as follows:
=0.16
Also, the Y-intercept is calculated as follows:
=75-0.15 x 280
=30.2
Hence, the equation of the least-squares line is:
Y=30.2+0.16X
Here, the slope b of above regression line (0.16) is the rate at which the predicted response Y changes among the line as the explanatory variable X changes. Specifically, b is the predicted change in Y when X increases by 1 unit.
Here b is positive; this shows of pre-exam totals increases by 1 mark then final examination score increases by 0.16 marks.
Conclusion:
Therefore, th equation of least-squares regression line is Y=30.2+0.16X
(b)
To predict: J’s final-exam score by using the regression line
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 6CRE
J’s final-exam scoreis 78.2.
Explanation of Solution
Calculation:
It is given that Julie’s pre-exam total was 300.
Then, the predicted final examination score is calculated as follows:
Julie’s predicted final examination score is 78.2.
Conclusion:
Hence, J’s final-exam score is 78.2.
(c)
the value of
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 6CRE
The value is R-square = 36%
Explanation of Solution
Calculation:
The
That is, r=0.6
Then
=0.36
That is, R-square=36%
Based on the value of R-square, we can say that 36% of the variation in final examination score is accounted for by the least-squares regression line of final examination score to pre-exam total.
That implies, 64% of the variation in final examination scores is unaccounted for by the linear relationship for these data. Professor Friedman’s prediction of Julie’s final examination score may not be very accurate.
Conclusion:
Hence,the value is R-square = 36%.
Chapter 3 Solutions
The Practice of Statistics for AP - 4th Edition
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