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Explanation & Answer
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x
2
3
6
7
8
7
9
y
12
9
8
7
6
5
2
y vs x
14
12
10
8
6
y = -1.125x + 13.75
R² = 0.8438
4
2
0
0
m
S-slope
r^2
F
SSR
n
-1.125
13.75 b
0.216506 1.398341 S-intercept
0.84375 1.369306 Sy/x
27
5 df
50.625
9.375 SSE
7
1 df (model
1
2
3
tcrit 0.95
4
5
6
7
2.015
df
MSM
MSE
Fcrit 0.95
50.625
1.875
6.61
1
5
8
a. The equation is y = -1.125x + 13.75
b. At 95% confidence:
Ho: b1 = 0;
Ha: b1 ≠ 0
tcalc
5.196152
tcalc > tcrit, reject Ho.
* At 95% confidence, the slope is significantly different from zero.
c. F-test
9
10
Ho: b1 = 0;
Ha: b1 ≠ 0
Fcalc
27
Fcalc > Fcrit, reject Ho.
* At 95% confidence, the regression model is significant.
d. The coefficient of determination is 0.8438.
This means that 84.38% of the variances can be accounted for by the model.
The model has a good linear fit.
x
2
3
6
7
8
7
9
y
12
9
8
7
6
5
2
y vs x
14
12
10
8
y = -1.125x + 13.75
R² = 0.8438
6
4
2
0
0
* The regression equation is y = -1.125x + 13.75
1
2
3
4
5
6
7
8
8
9
10
sum x
sum x^2
sum y
sum y^2
sum xy
n
154
2586
451
18901
5930
11
b0
b1
r squared
num
denom
53.50233
-0.89302
-4224
4618.69
a. Equation of the line: y = 53.50233 - 0.89302x
b.
r
-0.91454 r^2
0.836393
* The coefficient of determination is 0.836393
c. F-test
df
Ho: b1 = 0;
Ha: b1 ≠ 0
SSR
SST
SSE
342.9209
1 MSM
410
67.07907
10 MSE
Fcalc
51.1219
Fcrit 0.95
4.96
Fcalc > Fcrit; reject Ho.
* At 95% confidence, the regression model is significant.
342.9209
6.707907
d. T-test
tcrit 0.95
1.812
tcalc > tcrit; reject Ho.
tcalc
2.743635
* aT 95% confidence, the slope is significantly different from 0.
e. When the demand is 0,
0 = 53.50233 - 0.89302x
x = -53.50233/-0.89302
x
59.91146
Ho: b1 = 0;
Ha: b1 ≠ 0
* The demand is 0 when the price is $59.9.
Spxy
SSx
SSy
Sslope
xbar
ybar
-384
430
410
0.325489
14
41
ANOVA
Regression
Residual
Total
df
1
13
14
Coefficients
SS
50.58
55.42
106
Standard Error
Intercept
16.156
1.42
Variable x
-0.903
0.26
a.
t Stat
3.473076923
Ho: μx = μy = 0;
Ha: m...