The table below presents data on weight (x, in pounds) and price (y, in dollars) for 10 road-racing bikes.| Brand | Weight (pounds) | Price ($) ||-------|-----------------|-----------|| A | 17.8 | 2,100 || B | 16.1 | 6,250 || C | 14.9 | 8,370 || D | 15.9 | 6,200 || E | 17.2 | 4,000 || F | 13.1 | 8,500 || G | 16.2 | 6,000 || H | 17.1 | 2,680 || I | 17.6 | 3,400 || J | 14.1 | 8,000 |The estimated regression equation derived from these data is: \[ \hat{y} = 28,280 - 1,421x. \]Where:- $ \hat{y} $ represents the predicted price.- $ x $ represents the weight of the bike.For this dataset:- Sum of Squares for Error (SSE) = 7,062,767.99- Total Sum of Squares (SST) = 50,936,800Utilize the F test to determine whether there is a significant relationship between the weight of a bike and its price at the 0.05 level of significance.This table and analysis will aid in understanding how the weight of a road-racing bike might impact its price and help determine the statistical significance of this relationship. **Instructions for Statistical Analysis:**1. **Find the value of the test statistic.** (Round your answer to two decimal places.) [Input Box]2. **Find the p-value.** (Round your answer to three decimal places.) $ p\text{-value} = $ [Input Box]3. **State your conclusion.** - [ ] Reject $ H_0 $. We cannot conclude that the relationship between weight (pounds) and price (\$) is significant. - [x] Reject $ H_0 $. We conclude that the relationship between weight (pounds) and price (\$) is significant. - [ ] Do not reject $ H_0 $. We cannot conclude that the relationship between weight (pounds) and price (\$) is significant. - [ ] Do not reject $ H_0 $. We conclude that the relationship between weight (pounds) and price (\$) is significant.The option "Reject $ H_0 $. We conclude that the relationship between weight (pounds) and price (\$) is significant." is selected, indicating that there is enough statistical evidence to determine a significant relationship between weight and price.

Answered: Image /qna-images/answer/139dd450-cae4-4a7c-ac0a-96dd9cdd5534.jpg

Answered: Find the value of the test statistic.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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$The table below presents data on weight (x, in pounds) and price (y, in dollars) for 10 road-racing bikes. | Brand | Weight (pounds) | Price ($) | |-------|-----------------|-----------| | A | 17.8 | 2,100 | | B | 16.1 | 6,250 | | C | 14.9 | 8,370 | | D | 15.9 | 6,200 | | E | 17.2 | 4,000 | | F | 13.1 | 8,500 | | G | 16.2 | 6,000 | | H | 17.1 | 2,680 | | I | 17.6 | 3,400 | | J | 14.1 | 8,000 | The estimated regression equation derived from these data is: \[ \hat{y} = 28,280 - 1,421x. \] Where: - $ \hat{y} $ represents the predicted price. - $ x $ represents the weight of the bike. For this dataset: - Sum of Squares for Error (SSE) = 7,062,767.99 - Total Sum of Squares (SST) = 50,936,800 Utilize the F test to determine whether there is a significant relationship between the weight of a bike and its price at the 0.05 level of significance. This table and analysis will aid in understanding how the weight of a road-racing bike might impact its price and help determine the statistical significance of this relationship.$

Transcribed Image Text:The table below presents data on weight (x, in pounds) and price (y, in dollars) for 10 road-racing bikes. | Brand | Weight (pounds) | Price ($) | |-------|-----------------|-----------| | A | 17.8 | 2,100 | | B | 16.1 | 6,250 | | C | 14.9 | 8,370 | | D | 15.9 | 6,200 | | E | 17.2 | 4,000 | | F | 13.1 | 8,500 | | G | 16.2 | 6,000 | | H | 17.1 | 2,680 | | I | 17.6 | 3,400 | | J | 14.1 | 8,000 | The estimated regression equation derived from these data is: \[ \hat{y} = 28,280 - 1,421x. \] Where: - $ \hat{y} $ represents the predicted price. - $ x $ represents the weight of the bike. For this dataset: - Sum of Squares for Error (SSE) = 7,062,767.99 - Total Sum of Squares (SST) = 50,936,800 Utilize the F test to determine whether there is a significant relationship between the weight of a bike and its price at the 0.05 level of significance. This table and analysis will aid in understanding how the weight of a road-racing bike might impact its price and help determine the statistical significance of this relationship.