Consider the following data on x = weight (pounds) and y = price (5) for 10 road-

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The second slide is the first part of the question  and the first slide is the second part of the question

Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
p-value
State your conclusion.
O Do not reject H,. We cannot conclude that the relationship between weight (pounds) and price ($) is significant.
O Do not reject H. We conclude that the relationship between weight (pounds) and price ($) is significant.
O Reject H,: We conclude that the relationship between weight (pounds) and price ($) is significant.
O Reject H. We cannot conclude that the relationship between weight (pounds) and price ($) is significant.
0'
Transcribed Image Text:Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value State your conclusion. O Do not reject H,. We cannot conclude that the relationship between weight (pounds) and price ($) is significant. O Do not reject H. We conclude that the relationship between weight (pounds) and price ($) is significant. O Reject H,: We conclude that the relationship between weight (pounds) and price ($) is significant. O Reject H. We cannot conclude that the relationship between weight (pounds) and price ($) is significant. 0'
Consider the following data on x = weight (pounds) and y = price ($) for 10 road-racing bikes.
Brand
Weight
Price ($)
A
17.8
2,100
16.1
6,250
14.9
8,370
D.
15.9
6,200
17.2
4,000
F
13.1
8,600
16.2
6,000
H.
17.1
2,580
I
17.6
3,500
14.1
8,000
These data provided the estimated regression equation y 28,466- 1,432x. For these data, SSE = 7,141,227.05 and SST = 51,699,800. Use the F test to determine whether the weight for a bike and the price are related at the
0.05 level of significance.
State the null and alternative hypotheses.
O Ho: fo = 0
H: Bo 0
O Ho: B1 0
H: B1= 0
%3D
O Ho: B1 = 0
H: B1 0
O Ho: B1 0
O Ho: Bo 0
H Po 0
%3D
2:20 P
Transcribed Image Text:Consider the following data on x = weight (pounds) and y = price ($) for 10 road-racing bikes. Brand Weight Price ($) A 17.8 2,100 16.1 6,250 14.9 8,370 D. 15.9 6,200 17.2 4,000 F 13.1 8,600 16.2 6,000 H. 17.1 2,580 I 17.6 3,500 14.1 8,000 These data provided the estimated regression equation y 28,466- 1,432x. For these data, SSE = 7,141,227.05 and SST = 51,699,800. Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level of significance. State the null and alternative hypotheses. O Ho: fo = 0 H: Bo 0 O Ho: B1 0 H: B1= 0 %3D O Ho: B1 = 0 H: B1 0 O Ho: B1 0 O Ho: Bo 0 H Po 0 %3D 2:20 P
Expert Solution
Step 1

Given information:

Given data represents the values of the variables X = Weight and Y = Price for a sample of 10 brands.

The estimated regression equation is Y^ = 28466 – 1432*X.

The values of error sum of squares and total sum of squares is SSE = 7141227.05 and SST = 51699800.

Step 2

Test the significance of the model:

The investigator is interested to test whether the model is significant or not.

Denote β1 as the regression coefficient for the predictor variable X = weight.

The null and alternate hypotheses are stated below:

Null hypothesis H0:

H0: β1 = 0

That is, the regression model is not significant.

Alternative hypothesis H1:

H1: β1 ≠ 0

That is, the regression model is significant.

The level of significance is α = 0.05.

Test statistic:

Here, the total number of observations is N = 10 and the number of independent variables k = 1.

The F-statistic value is obtained as given below:

Statistics homework question answer, step 2, image 1

Thus, the F-test statistic value is F-statistic = 49.92.

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