Miles (1000s) Price ($1000s) 116.53 25.6 100.27 22.2 29.93 43.3 25.47 27.6 49.96 36.2 83.68 29.8 62.53 24.3 85.54 32.8 27.93 35.0 89.31 23.6 59.89 25.5 17.87 23.6 20.35 29.2 116.65 24.7 63.18 25.0 30.54 37.8 51.36 19.6 34.83 46.2 93.06 27.1 116.49 17.7 68.08 22.5 29.90 26.6 39.98 25.6 98.06 22.2 44.43 26.0 22.90 39.9 52.13 32.3 57.72 21.8 67.89 23.6 61.77 36.4 46.90 24.6 57.89 21.4 94.41 21.4 50.73 22.2 41.88 22.5 110.06 27.0 22.25 40.2 57.00 26.7 15.73 26.8 99.87 22.9 98.30 30.2 90.12 15.3 31.55 32.5 30.47 30.6 33.28 36.0 52.94 18.1 17.60 29.6 88.29 38.4 90.98 23.8 75.39 25.0 28.20 22.3 102.03 30.3 28.38 31.4 45.44 36.3 44.82 37.2 74.81 26.3 33.22 40.9 29.30 29.1 17.73 35.9 53.33 31.7 31.54 44.5 30.83 43.4 51.38 41.0 53.26 32.2 15.61 32.3 101.39 24.6 77.04 26.8 86.47 20.5 119.18 19.3 35.96 33.6 99.38 27.1 103.17 33.2 37.72 25.4 75.59 21.2 55.73 36.0 61.24 29.3 88.32 33.1 97.54 31.6 59.46 33.5 51.19 31.4 80.54 26.2 17.71 32.4 70.23 32.8 21.03 25.7 49.85 32.6 85.38 23.7 33.30 34.2 102.52 26.1 82.67 30.9 17.86 29.4 57.61 22.2 12.31 25.2 62.43 28.7 59.43 28.4 16.70 35.8 56.94 24.7 18.20 38.1 70.19 29.0 23.13 34.2 42.49 24.7 43.91 31.3 37.75 31.5 95.43 16.5 118.85 25.0 10.82 35.5 58.99 25.0 49.95 33.0 108.77 20.6 86.98 23.9 88.41 25.7 113.97 25.7 68.14 25.8 13.77 32.9 71.62 32.1 76.41 19.7 35.10 25.8 80.65 19.8 96.51 21.5 97.28 26.5 62.20 29.4 33.28 37.1 89.62 31.2 17.00 28.1 21.04 26.7 Develop an estimated linear regression equation showing how price in thousands of dollars (y) is related to miles in thousands (x). What is the estimated linear regression model? (Round your numerical values to four decimal places.) ŷ = 34.49−.0965·x (c) Test whether the parameter ?0 is equal to zero at a 0.01 level of significance. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. (Make your conclusion regardless of any validity concerns.) We reject H0. We can conclude that the y-intercept is not equal to zero.We reject H0. We cannot conclude that the y-intercept is not equal to zero. We fail to reject H0. We can conclude that the y-intercept is not equal to zero.We fail to reject H0. We cannot conclude that the y-intercept is not equal to zero. Test whether the parameter ?1 is equal to zero at a 0.01 level of significance. (Use the t test.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. (Make your conclusion regardless of any validity concerns.) We reject H0. We can conclude that there is a relationship between price and miles.We reject H0. We cannot conclude that there is a relationship between price and miles. We fail to reject H0. We cannot conclude that there is a relationship between price and miles.We fail to reject H0. We can conclude that there is a relationship between price and miles. What are the correct interpretations of the estimated parameters? b0 is our estimate of the miles in thousands when the price is zero. b1 is our estimate of the change in miles in thousands for a $1,000 increase in price.b0 is our estimate of the change in miles in thousands for a $1,000 increase in price. b1 is our estimate of the miles in thousands when the price is zero. b0 is our estimate of the price in thousands of dollars when the number of miles is zero. b1 is our estimate of the change in price in thousands of dollars for an increase of 1,000 miles.b0 is our estimate of the change in price in thousands of dollars for an increase of 1,000 miles. b1 is our estimate of the price in thousands of dollars when the number of miles is zero. Are these interpretations reasonable? The interpretation of b0 reasonable and the interpretation of b1 reasonable. (d) How much of the variation in the sample values of price (in %) does the model estimated in part (b) explain? (Round your answer to two decimal places.) % (e) For the model estimated in part (b), calculate the predicted price and residual for each automobile in the data. Identify the two automobiles that were the biggest bargains. (Round your answers to the nearest integer.) The best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price. The second best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price. (f) Suppose that you are considering purchasing a previously owned Camry that has been driven 105,000 miles. Use the estimated linear regression equation developed in part (b) to predict the price (in dollars) for this car. (Round your answer to the nearest integer.) $ Is this the price you would offer the seller?

Miles (1000s) Price ($1000s) 116.53 25.6 100.27 22.2 29.93 43.3 25.47 27.6 49.96 36.2 83.68 29.8 62.53 24.3 85.54 32.8 27.93 35.0 89.31 23.6 59.89 25.5 17.87 23.6 20.35 29.2 116.65 24.7 63.18 25.0 30.54 37.8 51.36 19.6 34.83 46.2 93.06 27.1 116.49 17.7 68.08 22.5 29.90 26.6 39.98 25.6 98.06 22.2 44.43 26.0 22.90 39.9 52.13 32.3 57.72 21.8 67.89 23.6 61.77 36.4 46.90 24.6 57.89 21.4 94.41 21.4 50.73 22.2 41.88 22.5 110.06 27.0 22.25 40.2 57.00 26.7 15.73 26.8 99.87 22.9 98.30 30.2 90.12 15.3 31.55 32.5 30.47 30.6 33.28 36.0 52.94 18.1 17.60 29.6 88.29 38.4 90.98 23.8 75.39 25.0 28.20 22.3 102.03 30.3 28.38 31.4 45.44 36.3 44.82 37.2 74.81 26.3 33.22 40.9 29.30 29.1 17.73 35.9 53.33 31.7 31.54 44.5 30.83 43.4 51.38 41.0 53.26 32.2 15.61 32.3 101.39 24.6 77.04 26.8 86.47 20.5 119.18 19.3 35.96 33.6 99.38 27.1 103.17 33.2 37.72 25.4 75.59 21.2 55.73 36.0 61.24 29.3 88.32 33.1 97.54 31.6 59.46 33.5 51.19 31.4 80.54 26.2 17.71 32.4 70.23 32.8 21.03 25.7 49.85 32.6 85.38 23.7 33.30 34.2 102.52 26.1 82.67 30.9 17.86 29.4 57.61 22.2 12.31 25.2 62.43 28.7 59.43 28.4 16.70 35.8 56.94 24.7 18.20 38.1 70.19 29.0 23.13 34.2 42.49 24.7 43.91 31.3 37.75 31.5 95.43 16.5 118.85 25.0 10.82 35.5 58.99 25.0 49.95 33.0 108.77 20.6 86.98 23.9 88.41 25.7 113.97 25.7 68.14 25.8 13.77 32.9 71.62 32.1 76.41 19.7 35.10 25.8 80.65 19.8 96.51 21.5 97.28 26.5 62.20 29.4 33.28 37.1 89.62 31.2 17.00 28.1 21.04 26.7 Develop an estimated linear regression equation showing how price in thousands of dollars (y) is related to miles in thousands (x). What is the estimated linear regression model? (Round your numerical values to four decimal places.) ŷ = 34.49−.0965·x (c) Test whether the parameter ?0 is equal to zero at a 0.01 level of significance. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. (Make your conclusion regardless of any validity concerns.) We reject H0. We can conclude that the y-intercept is not equal to zero.We reject H0. We cannot conclude that the y-intercept is not equal to zero. We fail to reject H0. We can conclude that the y-intercept is not equal to zero.We fail to reject H0. We cannot conclude that the y-intercept is not equal to zero. Test whether the parameter ?1 is equal to zero at a 0.01 level of significance. (Use the t test.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. (Make your conclusion regardless of any validity concerns.) We reject H0. We can conclude that there is a relationship between price and miles.We reject H0. We cannot conclude that there is a relationship between price and miles. We fail to reject H0. We cannot conclude that there is a relationship between price and miles.We fail to reject H0. We can conclude that there is a relationship between price and miles. What are the correct interpretations of the estimated parameters? b0 is our estimate of the miles in thousands when the price is zero. b1 is our estimate of the change in miles in thousands for a $1,000 increase in price.b0 is our estimate of the change in miles in thousands for a $1,000 increase in price. b1 is our estimate of the miles in thousands when the price is zero. b0 is our estimate of the price in thousands of dollars when the number of miles is zero. b1 is our estimate of the change in price in thousands of dollars for an increase of 1,000 miles.b0 is our estimate of the change in price in thousands of dollars for an increase of 1,000 miles. b1 is our estimate of the price in thousands of dollars when the number of miles is zero. Are these interpretations reasonable? The interpretation of b0 reasonable and the interpretation of b1 reasonable. (d) How much of the variation in the sample values of price (in %) does the model estimated in part (b) explain? (Round your answer to two decimal places.) % (e) For the model estimated in part (b), calculate the predicted price and residual for each automobile in the data. Identify the two automobiles that were the biggest bargains. (Round your answers to the nearest integer.) The best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price. The second best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price. (f) Suppose that you are considering purchasing a previously owned Camry that has been driven 105,000 miles. Use the estimated linear regression equation developed in part (b) to predict the price (in dollars) for this car. (Round your answer to the nearest integer.) $ Is this the price you would offer the seller?

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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Question

Miles (1000s)	Price ($1000s)
116.53	25.6
100.27	22.2
29.93	43.3
25.47	27.6
49.96	36.2
83.68	29.8
62.53	24.3
85.54	32.8
27.93	35.0
89.31	23.6
59.89	25.5
17.87	23.6
20.35	29.2
116.65	24.7
63.18	25.0
30.54	37.8
51.36	19.6
34.83	46.2
93.06	27.1
116.49	17.7
68.08	22.5
29.90	26.6
39.98	25.6
98.06	22.2
44.43	26.0
22.90	39.9
52.13	32.3
57.72	21.8
67.89	23.6
61.77	36.4
46.90	24.6
57.89	21.4
94.41	21.4
50.73	22.2
41.88	22.5
110.06	27.0
22.25	40.2
57.00	26.7
15.73	26.8
99.87	22.9
98.30	30.2
90.12	15.3
31.55	32.5
30.47	30.6
33.28	36.0
52.94	18.1
17.60	29.6
88.29	38.4
90.98	23.8
75.39	25.0
28.20	22.3
102.03	30.3
28.38	31.4
45.44	36.3
44.82	37.2
74.81	26.3
33.22	40.9
29.30	29.1
17.73	35.9
53.33	31.7
31.54	44.5
30.83	43.4
51.38	41.0
53.26	32.2
15.61	32.3
101.39	24.6
77.04	26.8
86.47	20.5
119.18	19.3
35.96	33.6
99.38	27.1
103.17	33.2
37.72	25.4
75.59	21.2
55.73	36.0
61.24	29.3
88.32	33.1
97.54	31.6
59.46	33.5
51.19	31.4
80.54	26.2
17.71	32.4
70.23	32.8
21.03	25.7
49.85	32.6
85.38	23.7
33.30	34.2
102.52	26.1
82.67	30.9
17.86	29.4
57.61	22.2
12.31	25.2
62.43	28.7
59.43	28.4
16.70	35.8
56.94	24.7
18.20	38.1
70.19	29.0
23.13	34.2
42.49	24.7
43.91	31.3
37.75	31.5
95.43	16.5
118.85	25.0
10.82	35.5
58.99	25.0
49.95	33.0
108.77	20.6
86.98	23.9
88.41	25.7
113.97	25.7
68.14	25.8
13.77	32.9
71.62	32.1
76.41	19.7
35.10	25.8
80.65	19.8
96.51	21.5
97.28	26.5
62.20	29.4
33.28	37.1
89.62	31.2
17.00	28.1
21.04	26.7

Develop an estimated linear regression equation showing how price in thousands of dollars (y) is related to miles in thousands (x). What is the estimated linear regression model? (Round your numerical values to four decimal places.)

ŷ =

34.49−.0965·x

(c)

Test whether the parameter ?₀ is equal to zero at a 0.01 level of significance.

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion. (Make your conclusion regardless of any validity concerns.)

We reject H₀. We can conclude that the y-intercept is not equal to zero.We reject H₀. We cannot conclude that the y-intercept is not equal to zero. We fail to reject H₀. We can conclude that the y-intercept is not equal to zero.We fail to reject H₀. We cannot conclude that the y-intercept is not equal to zero.

Test whether the parameter ?₁ is equal to zero at a 0.01 level of significance. (Use the t test.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion. (Make your conclusion regardless of any validity concerns.)

We reject H₀. We can conclude that there is a relationship between price and miles.We reject H₀. We cannot conclude that there is a relationship between price and miles. We fail to reject H₀. We cannot conclude that there is a relationship between price and miles.We fail to reject H₀. We can conclude that there is a relationship between price and miles.

What are the correct interpretations of the estimated parameters?

b₀ is our estimate of the miles in thousands when the price is zero. b₁ is our estimate of the change in miles in thousands for a $1,000 increase in price.b₀ is our estimate of the change in miles in thousands for a $1,000 increase in price. b₁ is our estimate of the miles in thousands when the price is zero. b₀ is our estimate of the price in thousands of dollars when the number of miles is zero. b₁ is our estimate of the change in price in thousands of dollars for an increase of 1,000 miles.b₀ is our estimate of the change in price in thousands of dollars for an increase of 1,000 miles. b₁ is our estimate of the price in thousands of dollars when the number of miles is zero.

Are these interpretations reasonable?

The interpretation of b₀ reasonable and the interpretation of b₁ reasonable.

(d)

How much of the variation in the sample values of price (in %) does the model estimated in part (b) explain? (Round your answer to two decimal places.)

(e)

For the model estimated in part (b), calculate the predicted price and residual for each automobile in the data. Identify the two automobiles that were the biggest bargains. (Round your answers to the nearest integer.)

The best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price.

The second best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price.

(f)

Suppose that you are considering purchasing a previously owned Camry that has been driven 105,000 miles. Use the estimated linear regression equation developed in part (b) to predict the price (in dollars) for this car. (Round your answer to the nearest integer.)

Is this the price you would offer the seller?

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