Math 227 Elementary Statistics-Minitab Handout Ch10
Ch10.
In Question #1- #5
a. Construct the scatter diagram.
b. Find the value of the linear correlation coefficient r.
c. Determine whether there is a significant linear correlation between the two variables.
d. If there is a positive/negative linear correlation, find the equation of the regression line.
e. Find the best predicted value for a requested x.
#1
Blood Pressure and Age: (Ch10 Section 10-2 Example 10-1) Open the data obtained in a
study of age and systolic blood pressure of six randomly selected subjects.
#2.
When bears were anesthetized, researchers measured the distances (in inches) around
their chests and they weighted the bears (in pounds). The results are given below for
eight male bears. Based on the results, does a bear’s weight seem to be related to its
chest size?
X Chest (in.)
Y Weight (lb.)
26
90
45
344
54
416
49
348
41
262
49
360
44
332
19
34
Find the best predicted weight of a bear with a chest size of 52 in.
#3
The accompanying table lists weights (in hundreds of pounds) and highway fuel usage
rates (in mi./gal) for a sample of domestic new cars. Based on the result, can you expect
to pay more for gas if you buy a heavier car?
X Weight
Y Fuel
29
31
35
27
28
29
44
25
25
31
43
29
30
28
33
28
28
28
24
33
Find the best predicted fuel consumption amount for a car that weights 4200 lb.
(Note that the table has values of x given in hundreds of pounds)
#4
The paired data below consist of weights (in pounds) of discarded paper and sizes of
households.
Paper
Household Size
2.41
2
7.57
3
9.55
3
8.82
6
8.72
4
6.96
2
6.83
1
11.42
5
What is the best predicted size of a household that discards 10.00 lb. of paper?
#5
A study was conducted to investigate a relationship between age (in years) and BAC
(blood alcohol concentration) measured when convicted DWI jail inmates were first
arrested. Sample dates are given below for randomly selected subjects. Based on the
result, does the BAC level seem to be related to the age of the person tested?
Age
BAC
17.2
0.19
43.5
0.20
30.7
0.26
53.1
0.16
37.2
0.24
21.0
0.20
27.6
0.18
46.3
0.23
What is the best predicted blood alcohol level of a person 21.0 years of age who has
been convicted and jailed for DWI? (The BAC level is measured when the person is first
arrested.)
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Math 227 Elementary Statistics-Minitab Handout Ch10
How to Do it:
Create a Scatter Plot
- Choose Graph > Scatterplot, then select Simple and click OK
- Double-click on an appropriate column for the “Y variables”
- Double-click on an appropriate column for the “X variables”
- Click Data View and choose Symbols for the Data Display. Click OK
- Click Label, type the label that you want it to be called, and click Ok twice
Calculate Correlation coefficient
- Choose Stat > Basic Statistics > Correlation
- Double-click the columns intended for the “Variables.” The box for Display p-values
should be checked.
- Click Ok
Find equation of the regression line
- Choose Stat > Regression > Regression
- Double-click the column intended for the “Response” variable Y.
- Double-click the column intended for the “Predictors” variable X.
- Click Ok
(Optional) Obtaining Residuals
- Choose Stat > Regression > Regression
- Click on Storage, then check the boxes for the Residuals and Fits.
- Click Ok twice
Computing Response Variable Estimates
- Choose Stat > Regression > Regression
- Double-click the column intended as the “Response” variable and the column intended
for the “Predictor” variable
- Click Options
- Type in value as the “Prediction intervals for new observations”
- Click Ok twice
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Math 227 Elementary Statistics-Minitab Handout Ch10
Answer Key Ch 10
#1.
a. Scatterplot of Pressure y vs Age x
Scatterplot of Pressure y vs Age x
155
F
150
145
D
Pressure y
E
140
C
135
130
A
125
B
120
40
45
50
55
Age x
60
65
70
b. Correlations: Pressure y, Age x
Pearson correlation of Pressure y and Age x = 0.897
P-Value = 0.015
(The null hypothesis would be rejected at a significance level of 0.015.)
c. There is a significant positive linear correlation between age and blood pressure since
r=0.897.
d.
Regression Analysis: Pressure y versus Age x
The regression equation is
Pressure y = 81.0 + 0.964 Age x
Predictor
Constant
Age x
Coef
81.05
0.9644
S = 5.64109
SE Coef
13.88
0.2381
R-Sq = 80.4%
T
5.84
4.05
P
0.004
0.015
R-Sq(adj) = 75.5%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
4
5
SS
522.21
127.29
649.50
Subject Age x Pressure y
A
43
128
MS
522.21
31.82
RESI1
5.48353
F
16.41
P
0.015
FITS1
122.516
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Math 227 Elementary Statistics-Minitab Handout Ch10
B
C
D
E
F
48
56
61
67
70
e.
New
Obs
1
120
135
143
141
152
-7.33838
-0.05343
3.12467
-4.66162
3.44524
127.338
135.053
139.875
145.662
148.555
Predicted Values for New Observations
Fit
129.27
SE Fit
2.91
95% CI
(121.18, 137.36)
95% PI
(111.64, 146.90)
Values of Predictors for New Observations
New
Obs
1
Age x
50.0
#2.
a. Scatterplot of Y Weight (lb.) vs X Chest (in.)
Scatterplot of Y Weight (lb.) vs X Chest (in.)
400
Y Weight (lb.)
300
200
100
0
20
25
30
35
40
X Chest (in.)
45
50
55
b. Correlations: Y Weight (lb.), X Chest (in.)
Pearson correlation of Y Weight (lb.) and X Chest (in.) = 0.993
P-Value = 0.000
There is a significant positive linear correlation between the distances around the chest and
weight of bears since r=0.993.
c.
d.
Regression Analysis: Y Weight (lb.) versus X Chest (in.)
The regression equation is
Y Weight (lb.) = - 187 + 11.3 X Chest (in.)
Predictor
Constant
Coef
-187.46
SE Coef
23.71
T
-7.91
P
0.000
4
Math 227 Elementary Statistics-Minitab Handout Ch10
X Chest (in.)
11.2713
S = 17.9445
0.5589
R-Sq = 98.5%
20.17
0.000
R-Sq(adj) = 98.3%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
6
7
SS
130963
1932
132896
MS
130963
322
F
406.71
X Chest (in.) Y Weight (lb.) RESI1
26
90
-15.5902
45
344
24.2561
54
416
-5.1852
49
348
-16.8289
41
262
-12.6589
49
360
-4.8289
44
332
23.5273
19
34
7.3086
e.
P
0.000
FITS1
105.590
319.744
421.185
364.829
274.659
364.829
308.473
26.691
Predicted Values for New Observations
New
Obs
1
Fit
398.64
SE Fit
8.88
95% CI
(376.91, 420.38)
95% PI
(349.65, 447.64)
Values of Predictors for New Observations
New
Obs
1
x Chest
52.0
#3.
a. Scatterplot of Y Fuel vs X Weight
Scatterplot of Y Fuel vs X Weight
33
32
31
Y Fuel
30
29
28
27
26
25
24
25
30
35
X Weight
40
45
5
Math 227 Elementary Statistics-Minitab Handout Ch10
b. Correlations: Y Fuel, X Weight
Pearson correlation of Y Fuel and X Weight = -0.710
P-Value = 0.022
c. There is a significant negative linear correlation between weights and highway fuel usage
rates for a sample of domestic new cars since r=-0.710.
d. Regression Analysis: Y Fuel versus X Weight
The regression equation is
Y Fuel = 36.3 - 0.234 X Weight
Predictor
Constant
X Weight
Coef
36.350
-0.23354
S = 1.70620
SE Coef
2.671
0.08200
T
13.61
-2.85
R-Sq = 50.3%
P
0.000
0.022
R-Sq(adj) = 44.1%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
8
9
SS
23.611
23.289
46.900
Unusual Observations
Obs X Weight Y Fuel
6
43.0 29.000
MS
23.611
2.911
Fit
26.308
F
8.11
SE Fit
1.058
P
0.022
Residual
2.692
St Resid
2.01R
R denotes an observation with a large standardized residual.
X Weight
29
31
35
27
28
29
44
25
25
31
43
29
30
28
33
28
28
28
24
33
Y Fuel RESI1 FITS1
1.42273
29.5773
-1.17602
28.1760
-0.81081
29.8108
-1.07415
26.0742
0.48857
30.5114
2.69231
26.3077
-1.34373
29.3437
-0.64310
28.6431
-1.81081
29.8108
2.25502
30.7450
e. Predicted Values for New Observations
New
Obs
1
Fit
26.541
SE Fit
0.988
95% CI
(24.262, 28.821)
95% PI
(21.994, 31.088)
Values of Predictors for New Observations
New
Obs
1
X Weight
42.0
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Math 227 Elementary Statistics-Minitab Handout Ch10
#4.
a. Scatterplot of Household Size y vs Paper x
Scatterplot of Household Size y vs Paper x
6
Household Size y
5
4
3
2
1
2
3
4
5
6
7
Paper x
8
9
10
11
b. Correlations: Household Size y, Paper x
Pearson correlation of Household Size y and Paper x = 0.630
P-Value = 0.094
There is no significant linear correlation between household size and paper since r= 0.630.
c.
Answers d and e omitted.
#5.
a.
Scatterplot of BAC y vs Age x
0.275
0.250
BAC y
0.225
0.200
0.175
0.150
15
20
25
30
35
Age x
40
45
50
55
.
b. Correlations: BAC y, Age x
Pearson correlation of BAC y and Age x = -0.069
P-Value = 0.871
c. There is no significant linear correlation between age and blood alcohol concentration since
r= -0.069
Answers d and e omitted.
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