BBUnderStat Week 7 Exercises: Regression Analysis Homework Solution

This document presents a complete solution to a statistics homework assignment focusing on regression analysis, as part of the BBUnderStat course. The assignment involves analyzing data related to the Denver job market, using concepts such as scatter plots, least squares regression lines, and correlation coefficients. The solution includes calculations for the sample means (x̄ and ȳ), the equation of the least-squares line, and the coefficient of determination (R-squared) for four different datasets. Each question's solution includes a scatter plot, the respective values, and the calculation of the least squares regression line. The document also provides interpretations of the R-squared values, explaining the explained and unexplained variance. Finally, the solution uses the regression equation to predict the value of y for a given value of x.

Question 12
(a) Scatter plot
10 15 20 25 30 35 40 45 50 55
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Scatter Plot
x
y
(b) Respective values
(c) X bar = 202/6 = 33.67
Y bar = 30/6 = 5.00
Least square regression line
y=−0.819+0.173 x
(d) Option D
(e) R square = 0.869
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Explained = 86.9%
Unexplained = 13.1%
(f) x = 36
y=−0.819+0.173 x=−0.819+ ( 0.173∗36 )
y=5.40 hundred jobs
Question 13
(a) Scatter plot
(b) Respective values
(c) X bar = 16/4 = 4.00
Y bar = 153/4 = 38.25
Least square regression line
y=57.679+(−4.857) x
(d) Option A
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(e) R square = 0.911
Explained = 91.1%
Unexplained = 8.9%
(f) x = 3
y=57.679+ (−4.857∗3 )=43.11 %
Question 14
(a)Scatter plot
(b)Respective values
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(c)X bar = 329/7 = 47.00
Y bar = 117/7 = 16.00
Least square regression line
y=37.486+(−0.457 x )
(d)Option B
(e)R square = 0.932
Explained = 93.2%
Unexplained = 6.8%
(f) x = 20
y=37.486+ (−0.457∗20 )=28.34 %
Question 15
(a) Scatter plot
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(b) Respective values
(c) X bar = 52.9/6 = 8.82
Y bar = 83.9/6 = 13.98
Least square regression line
y=−33.785+(5.418∗x)
(d) Option D
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(e) R square = 0.976
Explained = 97.6%
Unexplained = 2.4%
(f) x = 8.5
y=−33.785+ ( 5.418∗8.5 ) =12.27 M . D . s per 10,000residents
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