Homework SourseThe following data show the brand price and the overall sco
The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is = 24.9 + 0.301x, where x = price ($) and y = overall score.
Round your answers to three decimal places.
a. Compute SST, SSR, and SSE.
| Brand | Price | Score |
| Bose | 180 | 76 |
| Scullcandy | 150 | 71 |
| Koss | 95 | 62 |
| Phillips/O\'Neill | 70 | 57 |
| Denon | 70 | 30 |
| JVC | 35 | 34 |
Solution
The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is = 24.9 + 0.301x, where x = price ($) and y = overall score.
Brand
Price
Score
Bose
180
76
Scullcandy
150
71
Koss
95
62
Phillips/O\'Neill
70
57
Denon
70
30
JVC
35
34
Round your answers to three decimal places.
a. Compute SST, SSR, and SSE.
Mean of y=55
Price(x)
Score(y)
y pred
y-ymean
y-ypred
180
76
79.080
441
9.4864
150
71
70.050
256
0.9025
95
62
53.495
49
72.33503
70
57
45.970
4
121.6609
70
30
45.970
625
255.0409
35
34
35.435
441
2.059225
Total
1816.000
461.485
SST=1816
SSE=461.485
SSR= SST-SSE =1816-461.485=1354.515
Regression Analysis
r²
0.746
n
6
r
0.864
k
1
Std. Error
10.741
Dep. Var.
Score
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,354.515
1
1,354.5151
11.74
.0266
Residual
461.485
4
115.3712
Total
1,816.000
5
Regression output
confidence interval
variables
coefficients
std. error
t (df=4)
p-value
95% lower
95% upper
Intercept
24.8997
9.8183
2.536
.0643
-2.3604
52.1598
Price
0.3010
0.0878
3.426
.0266
0.0571
0.5449
| Brand | Price | Score |
| Bose | 180 | 76 |
| Scullcandy | 150 | 71 |
| Koss | 95 | 62 |
| Phillips/O\'Neill | 70 | 57 |
| Denon | 70 | 30 |
| JVC | 35 | 34 |
