Concept explainers
(a)
To find: the equation of the least-squares line
(a)
Answer to Problem 51E
The equation of the least-squares line is
Explanation of Solution
Given:
Mean | Standard deviation | |
IQ score | ||
Grade point average(GPA) |
Calculation:
The least-squares regression line is
Where
Slope
AndY intercept is
The least-squares regression line of the IQ score and GPA score has slope:
To find the intercept, we use the fact that the least-squares line passes through
So the equation of the least-squares line is:
Conclusion:
So the equation of the least-squares line is
(b)
To explain:percent of the variation in these students GPAs
(b)
Answer to Problem 51E
Then 40.16% of the variation in Y is due to the straight line relationship between Y and X. The other 59.84% is individual variation that is not explained by the linear relationship.
Explanation of Solution
Calculation:
The coefficient of determination
Here,
Then about 40.16% of the variation in Y is due to the straight line relationship between Y and X. The other 59.84% is individual variation that is not explained by the linear relationship.
Conclusion:
Hence, about 40.16% of the variation in Y is due to the straight line relationship between Y and X. The other 59.84% is individual variation that is not explained by the linear relationship.
(b)
To find and interpret: the residual for the students.
(b)
Answer to Problem 51E
The student is negative; this shows the data point lies below the line.
The student had a GPA that was 6.3211 points worse than expected for someone with an IQ of 103.
Explanation of Solution
Calculation:
The least-squares regression line of the IQ score and GPA score is:
Predicted GPA score for a student having IQ score 103 is
But observed value of GPA score for same student is
This residual is negative; this shows the data point lies below the line.
The student had a GPA that was 6.3211 points worse than expected for someone with an IQ of 103.
Conclusion:
Hence, the student had a GPA that was -6.3211 points worse than expected for someone with an IQ of 103.
Chapter 3 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Fundamentals of Statistics (5th Edition)
Statistics for Business and Economics (13th Edition)
Elementary Statistics Using Excel (6th Edition)
Basic Business Statistics, Student Value Edition (13th Edition)
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