STAT-UB.0103.04-Statistics for Business Control and Regression Models
December 9, 2015
Homework 8-due December 15
Reading: From MBS: 12.1-12.4, 12.6 (up to page 700), 12.7, 12.11-12.12
Lecture Notes #22
1) A survey of a random sample of 47 NYU undergraduate students was
conducted to investigate the relationship between Sleep=average sleep time
per night (in hours) and the following variables:
Study =average study time per day (in hours)
CupsCoffee =average number of cups of coffee consumed by a student
per day, and
Age (in years)
Answer questions below based on the Minitab output on the next two
pages.
a) Is the estimated multiple linear regression model of Sleep on the
variables listed above statistically significant at = 0 01? (State the relevant
hypothesis test and your conclusion)
b) Compute 2 of the multiple linear regression model and interpret it.
c) Which two explanatory variables are most highly correlated with each
other? Which two explanatory variables exhibit the smallest correlation?
d) Identify predictor(s) that are statistically significant at = 0 05 in
the simple regressions but are not statistically significant at = 0 05 in the
multiple regression. Give a reason for their lack of statistical significance in
the multiple regression.
e) The two-variable model with CupsCoffee and Study was chosen as
the final model. Interpret the coefficients in this model.
f ) Before fitting the multiple regression models the students hypothesized
that for every one cup increase in CupsCoffee, the expected decrease in
Sleep is 0.4 of an hour. Based on the final model were they correct? Answer
by constructing an appropriate 95% confidence interval.
g) Construct a 95% confidence interval for the average sleep time of
students who study 4 hours and drink 6 cups of coffee. Is this a valid
confidence interval? Explain.
1
Regression Analysis: Sleep versus Age, Study, Cupscoffee
The regression equation is
Sleep = 4.91 + 0.0449 Age + 0.231 Study – 0.357 Cupscoffee
Predictor
Constant
Age
Study
Cupscoffee
Coef
4.9100
0.04486
0.23083
-0.35740
SE Coef
0.8070
0.03955
0.07268
0.09061
T
6.08
1.13
3.18
-3.94
P
0.000
0.263
0.003
0.000
S = 0.852758
Analysis of Variance
Source
Regression
Residual Error
Total
DF
3
43
46
SS
20.6029
31.2694
51.8723
MS
6.8676
0.7272
F
9.44
P
0.000
Correlations: Sleep, Age, Study, Cupscoffee
Sleep
0.296
0.043
Cupscoffee
0.369
0.011
-0.410
0.004
Study
Age
0.390
0.007
Age
0.001
0.997
Study
0.155
0.297
Regression Analysis: Sleep versus Study, Cupscoffee
The regression equation is
Sleep = 5.75 + 0.262 Study – 0.364 Cupscoffee
Predictor
Constant
Study
Cupscoffee
Coef
5.7544
0.26166
-0.36377
S = 0.855534
SE Coef
0.3130
0.06763
0.09073
R-Sq = 37.9%
T
18.39
3.87
-4.01
P
0.000
0.000
0.000
R-Sq(adj) = 35.1%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
2
44
46
SS
19.6671
32.2053
51.8723
MS
9.8335
0.7319
F
13.43
P
0.000
Predicted Values for New Observations
New
Obs
1
Fit
SE Fit
0.417
Values of Predictors for New Observations
New
Obs
1
Study
4.00
Cupscoffee
6.00
Descriptive Statistics: Sleep, Study, Cupscoffee
Variable
Sleep
Study
Cupscoffee
N
47
47
47
N*
0
0
0
Variable
Sleep
Study
Cupscoffee
Maximum
9.000
10.000
8.000
Mean
6.213
4.000
1.617
SE Mean
0.155
0.275
0.205
StDev
1.062
1.888
1.407
Minimum
4.000
1.000
0.000
Q1
5.000
3.000
1.000
Median
6.000
4.000
1.000
Q3
7.000
5.000
2.000
