Question

Use the table of values to find the line of regression and if justified at the 0.05 significance level, use it to find the predicted quality score of a TV set with a price of $1900. If the data does not suggest linear correlation, then use the average quality score as a prediction.

Price: 2,300, 1,800, 2,500, 2,700, 2,000, 1,700, 1,500, 2,700
Quality Score: 74, 73, 70, 66, 63, 62, 52, 68

Answer 1

y=48.2+0.00829x;64

Explanation:

Answer 2

Explanation:

no x y xy x²

1 2300 74 170200 5290000

2 1800 73 131400 3240000

3 2500 70 175000 6250000

4 2700 66 178200 7290000

5 2000 63 126000 4000000

6 1700 62 105400 2890000

7 1500 52 78000 2250000

8 2700 68 183600 7290000

Total 17200 528 1147800 38500000

Mean of x is

`\bar x = (17200)/(8) =2150`

Mean of y is

`\bar y = (528)/(8) =66`

From the table above

we find
`\hat B_1`

`\hat B_1=(\sum xy- \bar x \sum y)/(\sum x^2- n \barx^2) \\\\=(1147800-2150(528))/(38500000-8(2150)^2) \\\\=(1147800-1135200)/(38500000-36980000) \\\\=(12600)/(1520000) \\\\=0.008289`

so
`\hat b_0` is

`\hat b_0=\bar y-\bar B_1 x\\\\=66-0.008289(2150)\\\\=66-17.82135\\\\=48.17865`

The line of regression is

The price x is 1900

`\hat y =\hat B_0+\hat B_1x\\\\=48.17865+0.008289*1900\\\\=48.17865+15.7491\\\\=63.928`

The line of regression is 63.928