The variables are per capita cigarette consumption in 1930 (the independent vari
ID: 3042459 • Letter: T
Question
The variables are per capita cigarette consumption in 1930 (the independent variable, “X”) and the death rate from lung cancer in 1950 (the dependent variable, “Y”). The cancer rates are shown for a later time period because it takes time for lung cancer to develop and be diagnosed.
Observation #
Country
Cigarettes consumed
per capita in 1930 (X)
Lung cancer deaths per
million people in 1950 (Y)
1. The standard deviations of X and Y.
2. The correlation coefficient, r, between X and Y.
3. b1, the OLS estimated slope coefficient from the regression Yi=0+1Xi+ui.Yi=0+1Xi+ui.
4. b0, the OLS estimated intercept term from the same regression.
5. Y i,i=i,...,nY^i,i=i,...,n, the predicted values for each country from the regression.
6. u iu^i, the OLS residual for each country.
7. The R2.
8. The SER.
Observation #
Country
Cigarettes consumed
per capita in 1930 (X)
Lung cancer deaths per
million people in 1950 (Y)
Explanation / Answer
Answer:
1. The standard deviations of X and Y.
Descriptive statistics
x
y
n
5
5
mean
736.00
276.00
sample standard deviation
364.41
132.35
sample variance
132,792.50
17,517.50
minimum
380
150
maximum
1145
465
range
765
315
2. The correlation coefficient, r, between X and Y.
r=0.926
3. b1, the OLS estimated slope coefficient from the regression Yi=0+1Xi+ui.Yi=0+1Xi+ui.
b1=0.3364
4. b0, the OLS estimated intercept term from the same regression.
bo=28.3966
5. Y i,i=i,...,nY^i,i=i,...,n, the predicted values for each country from the regression.
Observation
y
Predicted
1
250.0
206.7
2
350.0
403.5
3
465.0
413.6
4
150.0
200.0
5
165.0
156.2
6. u iu^i, the OLS residual for each country.
Observation
y
Predicted
Residual
1
250.0
206.7
43.3
2
350.0
403.5
-53.5
3
465.0
413.6
51.4
4
150.0
200.0
-50.0
5
165.0
156.2
8.8
7. The R2.
R2 = 0.858
8. The SER.
SER=57.602
Regression Analysis
r²
0.858
n
5
r
0.926
k
1
Std. Error
57.602
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
60,116.1644
1
60,116.1644
18.12
.0238
Residual
9,953.8356
3
3,317.9452
Total
70,070.0000
4
Regression output
confidence interval
variables
coefficients
std. error
t (df=3)
p-value
95% lower
95% upper
Intercept
28.3966
63.6183
0.446
.6856
-174.0652
230.8583
x
0.3364
0.0790
4.257
.0238
0.0849
0.5879
Observation
y
Predicted
Residual
1
250.0
206.7
43.3
2
350.0
403.5
-53.5
3
465.0
413.6
51.4
4
150.0
200.0
-50.0
5
165.0
156.2
8.8
Descriptive statistics
x
y
n
5
5
mean
736.00
276.00
sample standard deviation
364.41
132.35
sample variance
132,792.50
17,517.50
minimum
380
150
maximum
1145
465
range
765
315
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