Intro Stats
4th Edition
ISBN: 9780321826275
Author: Richard D. De Veaux
Publisher: PEARSON
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Textbook Question
Chapter R, Problem 6.29RE
Hard water In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, or ppm) in the drinking water. Here are the
Dependent variable is Mortality
R-squared = 43%
s = 143.0 with 61 - 2 = 59 degrees of freedom
Variable | Coefficient | SE(Coeff) |
Intercept | 1676 | 29.30 |
Calcium | –3.23 | 0.48 |
- a) Is there an association between the hardness of the water and the mortality rate? Write the appropriate hypothesis.
- b) Assuming the assumptions for regression inference are met, what do you conclude?
- c) Create a 95% confidence interval for the slope of the true line relating calcium concentration and mortality.
- d) Interpret your interval in context.
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In a study of the performance of a new engine design, the weight of 12 cars (in pounds) and the top speed (in mph) were recorded. A regression line was generated and shown to be an appropriate description of the
relationship. The results of the regression analysis are below.
Depend Variable: Top Speed
Variable
Constant
Coefficient
107.58
s.e. of Coeff
t-ratio
prob
Weight
0.8710
11.12
0.4146
9.67
0.000
2.10
0.062
R squared = 30.6% R squared (adjusted) = 23.7%
s = 10.42 with 12-2 = 10 degrees of freedom
Part A: Provide the regression equation based off the analysis provided & explain it in context.
Part B: List the conditions for inference that need to be verified. Assuming these conditions have been met, does the data provide convincing evidence of a relationship between weight and top speed?
Part C: Assuming all conditions for inference have been verified, determine a 95% confidence interval estimate for the slope of the regression line.
A researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016:
??=?+????+????+???I
Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:
Predictor
Coef
StDev
t-ratio
p-value
Constant
5491.38
2508.81
2.1888
0.0491
Oil
85.39
18.46
4.626
0.0006
EXP
-377.08
112.19
*
0.0057
FDI
-396.99
160.66
-2.471
**
S = 2.45 R – sq = 96.3% R – sq (adj) = 95.3%
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
3
1991.31
663.77
?
??
Error
12
77.4
6.45
Total
15
e) Perform the F Test making sure to state…
We wish to determine if there is a correlation between the birth weight (in grams) of nine newborn infants and the length of their mothers’ stay (in days) in the hospital. The results of a correlation and regression analysis are indicated in the Excel output below. The mean birth weight of the newborn infants (the independent variable) was 3162.5 grams, and the mean length of their mothers’ stay in the hospital (the dependent variable) was 7 days.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.862675
R Square
0.744208
Adjusted R Square
0.707666
Standard Error
6.02142
Observations
9
ANOVA
df
SS
MS
F
Significance F
Regression
1
738.4198
738.4198
20.36599
0.002756
Residual
7
253.8025
36.25749
Total
8
992.2222…
Chapter R Solutions
Intro Stats
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