Response to the following questions:
1. Jason believes that sales of coffee at his shop depend on weather. He has taken a sample of 6 days. Results are shown in columns B and C of the table. I have also performed some computations to make you task easier.
|
Column A
|
Column B
|
Column
C
|
Column
D
|
Column E
|
Column
F
|
Column G
|
Column
H
|
|
|
cups of
coffee
|
Temp.
|
B minus its mean value
|
C minus its mean value
|
D x E
|
D^2
|
E^2
|
|
|
350
|
50
|
190
|
-25
|
-4750
|
36100
|
625
|
|
|
200
|
60
|
40
|
-15
|
-600
|
1600
|
225
|
|
|
210
|
70
|
50
|
-5
|
-250
|
2500
|
25
|
|
|
100
|
80
|
-60
|
5
|
-300
|
3600
|
25
|
|
|
60
|
90
|
-100
|
15
|
-1500
|
10000
|
225
|
|
|
40
|
100
|
-120
|
25
|
-3000
|
14400
|
625
|
|
sum
|
960
|
450
|
0
|
0
|
-10400
|
68200
|
1750
|
|
mean
|
160
|
75
|
|
|
|
|
|
a. Mark the space for the dependent variable (Y): ___ cups of coffee, ___ temperature
b. Compute the equation for the least squares regression line, and report on the line provided:
c. What is the slope of the estimated regression line? ________
d. In one sentence, what does the slope indicate?
e. Compute the coefficient of determination and the correlation coefficient for temperature and the sales of coffee. Report your answers here in the spaces provided:
r2 = ____________, r = ____________
f. Predict sales of a 90 degree day: _______________ cups .
g. Develop a 95% confidence interval for predicting average cups of coffee sold on a day when temperature is 90. Assume standard error of the estimate is 39.98.
2. Age and number of hours worked per week were used to predict GPA of students. Below you will see the Excel printout. Predict GPA of a 22-year old student who works 30 hours per week. Also, report what percentage of variability in GPA is explained by the multiple regression line.
Choose the letter corresponding to your answer from among the following and record it here: _______
A. GPA is 3.2 an variability explained is 72%
B. GPA is 3.2 and variability explained is 85%
C. GPA is 2.36 and variability explained is 48%
D. GPA is 2.36, variability explained is 43%
SUMMARY OUTPUT
|
Regression Statistics
|
|
Multiple R
|
0.85
|
|
R Square
|
0.72
|
|
Adjusted R Square
|
0.43
|
|
Standard Error
|
0.48
|
|
Observations
|
5
|
|
ANOVA
|
|
|
|
|
|
|
|
df
|
SS
|
MS
|
F
|
Significance F
|
|
Regression
|
2
|
1.16
|
0.5780
|
2.5365
|
0.2827693
|
|
Residual
|
2
|
0.46
|
0.2279
|
|
|
|
Total
|
4
|
1.61
|
|
|
|
|
|
Coefficients
|
Standard Error
|
t Stat
|
P-value
|
Lower 95%
|
Upper 95%
|
|
Intercept
|
0.96
|
1.15
|
0.8352
|
0.4915
|
-3.9999478
|
5.926914
|
|
Age
|
0.2
|
0.09
|
2.2287
|
0.1556
|
-0.1834896
|
0.577886
|
|
hours
|
-0.1
|
0.04
|
-2.1401
|
0.1657
|
-0.2892895
|
0.097099
|
3. Quarterly billing for two years of water usage is shown below.
|
|
Year
|
|
Quarters
|
1
|
2
|
|
Winter
|
64
|
66
|
|
Spring
|
103
|
103
|
|
Summer
|
152
|
160
|
|
Fall
|
73
|
72
|
|
|
De-seasonalized series
|
|
|
Year
|
|
Quarters
|
1
|
2
|
|
Winter
|
|
|
|
Spring
|
|
|
|
Summer
|
|
|
|
Fall
|
|
|
Seasonal indexes for this problem are calculated and reported in the table below.
|
Winter
|
Spring
|
Summer
|
Fall
|
|
0.67
|
1.03
|
1.56
|
0.75
|
b. Use seasonal indexes to de-seasonalize the time series. Report your results in the above blank table.
c. Trend equation was calculated for the de-seasonalized data. The equation is: T = 97.3 + 0.32t. Forecast ONLY summer billing for year 3: Report answer here: ___________ Show work in this space:
d. Use MAD as a measure of accuracy to determine overall effectiveness of this forecasting model. In your analysis, only include year 2. Fill out table below. Report MAD here: _____________
t y Forecast Show me how you calculated the Forecast Absolute Error
5 66
6 103
7 160
8 72
e. In ONE sentence, interpret the MAD value you calculated.