Stat 133 Recitation Solutions
2.3 and 2.4
Regression (Part 1) (SOLUTIONS)
We are comparing years of education and hours on the internet in the last month, to see
if a relationship exists. If a relationship does exist, we want to predict Internet use using
education level. The output is given below.
Descriptive Statistics: Education, Internet
Variable
Mean
StDev
Variance
Minimum
Maximum
Educatio
11.000
1.920
3.687
7.000
17.000
Internet
26.316
9.411
88.570
2.000
54.000
Pearson’s Correlation: 0.642
1. Interpret the correlation between Education and Internet use
As Education increases so does internet use; the relationship is linear (need to check
the scatterplot) but its strength is only moderate.
2. Would a line fit this data well? Explain by interpreting the correlation.
A line would fit moderately well.
3.
Define which variable is X and which one is Y.
X is education since it is being used to predict Internet use (Y)
4.
Find the slope of the best fitting line.
b
=
r
s
y
s
x
=
.642
9.411
1.920
The slope is 3.15
This means as education increases by 1 year, internet usage increases by 3.15 hrs per
month on average.
5. Find the Yintercept of the best fitting line.
a
=
y

bx
=
26.316

11 3.15
(
29
The Yintercept is 8.29
This is not interpretable
.
6. Find the equation of the best fitting line.
Internet Use = 8.29 + 3.15 (Education)
7. Use the line to predict Internet use for someone with 16 years of education.
Internet Use = 8.29 + 3.15 (16) = 42.11 hours per month (on average)
*8. For what education levels is it appropriate to use this line to make predictions? Use the
statistics given in the problem to answer this.
Using the following row of the descriptive statistics for education given in the
problem, you see that Education for the data collected is from 7 to 17 years. This is
the range where you would feel most comfortable using Education (X) to predict
Internet use (Y).
Variable
Mean
StDev
Variance
Minimum
Maximum
Educatio
11.000
1.920
3.687
7.000
17.000
1
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View Full DocumentStat 133 Recitation Solutions
2.3 and 2.4
9. The linear regression of the computer output for the Internet/Education data is shown
below. Use this output to find the equation of the best fitting line and use it to verify your
answer to #6 above.
Predictor
Coef
SE Coef
T
P
Constant
8.290
2.665
3.11
0.002
Education
3.1460
0.2387
13.18
0.000
Pick off the line from this output to be 8.29 + 3.15(X) = Y and verify your answer to
#6
.
Data was collected on amount of rainfall (inches) and amount of corn produced (bushels
per acre) for a number of years in Kansas. The output is shown below.
Predictor
Coef
SE Coef
T
P
Constant
89.543
6.703
13.36
0.000
Rainfall
0.12800
0.01375
9.31
0.000
Correlation of Rainfall and Corn = 0.608
10. If rainfall increases by 1 inch, how much do you predict corn production will change
by?
a. 89.543 bushels per acre
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 Fall '07
 rumseyjohnson
 Statistics, Econometrics, Linear Regression, Regression Analysis, Descriptive statistics

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