Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snell "SA" (Sports Application)-rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. Suppose the following data show the weight and price for 18 SA helmets. Weight (oz) Price ($) 64 248 64 278 64 200 64 200 58 300 47 700 49 900 59 340 66 199 58 299 58 299 52 469 52 479 63 359 62 369 54 549 63 250 63 280 (a) Develop a scatter diagram with weight as the independent variable. A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The points are plotted diagonally from the top left of the diagram to the bottom right and become less scattered as weight increases. The points are between 47 to 66 on the horizontal axis and between 50 to 800 on the vertical axis. A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The points are plotted from the bottom left of the diagram in an upward, diagonal direction that becomes steeper as weight increases. The points are between 47 to 66 on the horizontal axis and between 150 to 900 on the vertical axis. They are all plotted close together with very little scatter. A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The 7 leftmost points are between 47 to 59 on the horizontal axis and between 150 to 500 on the vertical axis. The remaining points are located between 62 to 66 on the horizontal axis and between 150 to 900 on the vertical axis. The points are fairly scattered. A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The points are plotted diagonally from the top left of the diagram to the bottom right and become less scattered as weight increases. The points are between 47 to 66 on the horizontal axis and between 150 to 900 on the vertical axis. (b) Does there appear to be any relationship between these two variables? There appears to be no noticeable relationship between weight (oz) and price ($).There appears to be a positive linear relationship between weight (oz) and price ($). There appears to be a negative linear relationship between weight (oz) and price ($). (c) Develop the estimated regression equation that could be used to predict the price ($) given the weight (oz). (Round your value for the y-intercept to the nearest integer and your value for the slope to two decimal places.) ŷ = (d) Test for the significance of the relationship at the 0.05 level of significance. (Use the F test.) State the null and alternative hypotheses. H0: ?1 ≠ 0 Ha: ?1 = 0H0: ?0 = 0 Ha: ?0 ≠ 0 H0: ?1 = 0 Ha: ?1 ≠ 0H0: ?1 ≥ 0 Ha: ?1 < 0H0: ?0 ≠ 0 Ha: ?0 = 0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject H0. We conclude that the relationship between weight (oz) and price ($) is significant.Do not reject H0. We cannot conclude that the relationship between weight (oz) and price ($) is significant. Reject H0. We conclude that the relationship between weight (oz) and price ($) is significant.Reject H0. We cannot conclude that the relationship between weight (oz) and price ($) is significant. (e) Did the estimated regression equation provide a good fit? Explain. (Round your answer to three decimal places.) Since r2 = is , the estimated regression equation a good fit

Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snell "SA" (Sports Application)-rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. Suppose the following data show the weight and price for 18 SA helmets. Weight (oz) Price ($) 64 248 64 278 64 200 64 200 58 300 47 700 49 900 59 340 66 199 58 299 58 299 52 469 52 479 63 359 62 369 54 549 63 250 63 280 (a) Develop a scatter diagram with weight as the independent variable. A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The points are plotted diagonally from the top left of the diagram to the bottom right and become less scattered as weight increases. The points are between 47 to 66 on the horizontal axis and between 50 to 800 on the vertical axis. A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The points are plotted from the bottom left of the diagram in an upward, diagonal direction that becomes steeper as weight increases. The points are between 47 to 66 on the horizontal axis and between 150 to 900 on the vertical axis. They are all plotted close together with very little scatter. A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The 7 leftmost points are between 47 to 59 on the horizontal axis and between 150 to 500 on the vertical axis. The remaining points are located between 62 to 66 on the horizontal axis and between 150 to 900 on the vertical axis. The points are fairly scattered. A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The points are plotted diagonally from the top left of the diagram to the bottom right and become less scattered as weight increases. The points are between 47 to 66 on the horizontal axis and between 150 to 900 on the vertical axis. (b) Does there appear to be any relationship between these two variables? There appears to be no noticeable relationship between weight (oz) and price ($).There appears to be a positive linear relationship between weight (oz) and price ($). There appears to be a negative linear relationship between weight (oz) and price ($). (c) Develop the estimated regression equation that could be used to predict the price ($) given the weight (oz). (Round your value for the y-intercept to the nearest integer and your value for the slope to two decimal places.) ŷ = (d) Test for the significance of the relationship at the 0.05 level of significance. (Use the F test.) State the null and alternative hypotheses. H0: ?1 ≠ 0 Ha: ?1 = 0H0: ?0 = 0 Ha: ?0 ≠ 0 H0: ?1 = 0 Ha: ?1 ≠ 0H0: ?1 ≥ 0 Ha: ?1 < 0H0: ?0 ≠ 0 Ha: ?0 = 0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject H0. We conclude that the relationship between weight (oz) and price ($) is significant.Do not reject H0. We cannot conclude that the relationship between weight (oz) and price ($) is significant. Reject H0. We conclude that the relationship between weight (oz) and price ($) is significant.Reject H0. We cannot conclude that the relationship between weight (oz) and price ($) is significant. (e) Did the estimated regression equation provide a good fit? Explain. (Round your answer to three decimal places.) Since r2 = is , the estimated regression equation a good fit

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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Related questions

Question

Weight (oz)	Price ($)
64	248
64	278
64	200
64	200
58	300
47	700
49	900
59	340
66	199
58	299
58	299
52	469
52	479
63	359
62	369
54	549
63	250
63	280

(a)

Develop a scatter diagram with weight as the independent variable.

A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The points are plotted diagonally from the top left of the diagram to the bottom right and become less scattered as weight increases. The points are between 47 to 66 on the horizontal axis and between 50 to 800 on the vertical axis.

A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The points are plotted from the bottom left of the diagram in an upward, diagonal direction that becomes steeper as weight increases. The points are between 47 to 66 on the horizontal axis and between 150 to 900 on the vertical axis. They are all plotted close together with very little scatter.

A scatter diagram has a number of points plotted on it. The horizontal axis ranges from 45 to 70 and is labeled: Weight (oz). The vertical axis ranges from 0 to 1,000 and is labeled: Price ($). The 7 leftmost points are between 47 to 59 on the horizontal axis and between 150 to 500 on the vertical axis. The remaining points are located between 62 to 66 on the horizontal axis and between 150 to 900 on the vertical axis. The points are fairly scattered.

(b)

Does there appear to be any relationship between these two variables?

There appears to be no noticeable relationship between weight (oz) and price ($).There appears to be a positive linear relationship between weight (oz) and price ($). There appears to be a negative linear relationship between weight (oz) and price ($).

(c)

Develop the estimated regression equation that could be used to predict the price ($) given the weight (oz). (Round your value for the y-intercept to the nearest integer and your value for the slope to two decimal places.)

ŷ =

(d)

Test for the significance of the relationship at the 0.05 level of significance. (Use the F test.)

State the null and alternative hypotheses.

H₀: ?₁ ≠ 0
H_a: ?₁ = 0H₀: ?₀ = 0
H_a: ?₀ ≠ 0 H₀: ?₁ = 0
H_a: ?₁ ≠ 0H₀: ?₁ ≥ 0
H_a: ?₁ < 0H₀: ?₀ ≠ 0
H_a: ?₀ = 0

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.

Do not reject H₀. We conclude that the relationship between weight (oz) and price ($) is significant.Do not reject H₀. We cannot conclude that the relationship between weight (oz) and price ($) is significant. Reject H₀. We conclude that the relationship between weight (oz) and price ($) is significant.Reject H₀. We cannot conclude that the relationship between weight (oz) and price ($) is significant.

(e)

Did the estimated regression equation provide a good fit? Explain. (Round your answer to three decimal places.)

Since

r² =

is , the estimated regression equation a good fit

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Weight (oz)	Price ($)
64	248
64	278
64	200
64	200
58	300
47	700
49	900
59	340
66	199
58	299
58	299
52	469
52	479
63	359
62	369
54	549
63	250
63	280

Weight (oz)	Price ($)
64	248
64	278
64	200
64	200
58	300
47	700
49	900
59	340
66	199
58	299
58	299
52	469
52	479
63	359
62	369
54	549
63	250
63	280

Weight (oz)	Price ($)
64	248
64	278
64	200
64	200
58	300
47	700
49	900
59	340
66	199
58	299
58	299
52	469
52	479
63	359
62	369
54	549
63	250
63	280