Hours Spent Studying Total Points Earned 22 12 20 18 29 25 24 25 43 28 46 29 39 35 40 39 51 40 43 43 39 43 51 49 52 50 65 51 57 53 56 53 52 55 66 55 63 57 68 57 67 59 42 59 65 59 69 60 72 60 66 61 53 61 45 61 58 62 81 62 60 62 57 62 77 62 78 63 67 64 78 64 72 64 58 64 71 65 76 65 79 66 83 66 65 66 72 66 71 66 52 67 78 67 70 67 81 67 80 68 79 68 72 68 75 68 91 68 65 68 84 69 77 69 78 70 72 70 84 70 83 70 67 70 80 71 78 71 72 72 70 72 94 72 92 72 84 73 98 73 78 73 78 73 84 73 74 74 90 74 83 74 84 74 83 75 78 75 93 75 80 75 101 76 81 76 83 76 91 76 83 76 93 76 78 76 78 77 65 77 84 77 97 77 88 77 93 78 93 78 95 78 95 79 91 79 95 79 94 79 95 80 102 80 105 80 83 80 99 80 97 81 79 81 101 81 88 82 93 83 95 85 94 85 104 85 88 85 80 86 98 86 83 86 91 86 90 87 83 87 92 88 88 88 99 89 101 90 101 90 99 90 102 90 84 90 110 91 93 91 105 91 109 91 91 92 104 92 95 92 98 92 91 93 104 93 104 94 106 95 95 95 106 95 92 95 101 96 95 96 109 96 95 96 101 96 105 97 104 97 104 97 105 98 95 99 109 100 110 100 101 100 Develop an estimated linear regression equation showing how total points earned (y) is related to hours spent studying (x). What is the estimated linear regression model? (Round your numerical values to four decimal places.) ŷ = (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 fail to reject H0. We cannot 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. 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 fail to reject H0. We cannot conclude that there is a relationship between hours spent studying and total points earned.We reject H0. We can conclude that there is a relationship between hours spent studying and total points earned. We reject H0. We cannot conclude that there is a relationship between hours spent studying and total points earned.We fail to reject H0. We can conclude that there is a relationship between hours spent studying and total points earned. What are the correct interpretations of the estimated parameters? b0 is our estimate of the hours spent studying when total points earned is zero. b1 is our estimate of the change in hours spent studying for a one point increase in total points earned.b0 is our estimate of the change in total points earned for a one hour increase in time spent studying. b1 is our estimate of the total points earned when the hours spent studying is zero. b0 is our estimate of the change in hours spent studying for a one point increase in total points earned. b1 is our estimate of the hours spent studying when total points earned is zero.b0 is our estimate of the total points earned when the hours spent studying is zero. b1 is our estimate of the change in total points earned for a one hour increase in time spent studying. 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 total points earned (in %) does the model you estimated in part (b) explain? (Round your answer to two decimal places.) %

Hours Spent Studying Total Points Earned 22 12 20 18 29 25 24 25 43 28 46 29 39 35 40 39 51 40 43 43 39 43 51 49 52 50 65 51 57 53 56 53 52 55 66 55 63 57 68 57 67 59 42 59 65 59 69 60 72 60 66 61 53 61 45 61 58 62 81 62 60 62 57 62 77 62 78 63 67 64 78 64 72 64 58 64 71 65 76 65 79 66 83 66 65 66 72 66 71 66 52 67 78 67 70 67 81 67 80 68 79 68 72 68 75 68 91 68 65 68 84 69 77 69 78 70 72 70 84 70 83 70 67 70 80 71 78 71 72 72 70 72 94 72 92 72 84 73 98 73 78 73 78 73 84 73 74 74 90 74 83 74 84 74 83 75 78 75 93 75 80 75 101 76 81 76 83 76 91 76 83 76 93 76 78 76 78 77 65 77 84 77 97 77 88 77 93 78 93 78 95 78 95 79 91 79 95 79 94 79 95 80 102 80 105 80 83 80 99 80 97 81 79 81 101 81 88 82 93 83 95 85 94 85 104 85 88 85 80 86 98 86 83 86 91 86 90 87 83 87 92 88 88 88 99 89 101 90 101 90 99 90 102 90 84 90 110 91 93 91 105 91 109 91 91 92 104 92 95 92 98 92 91 93 104 93 104 94 106 95 95 95 106 95 92 95 101 96 95 96 109 96 95 96 101 96 105 97 104 97 104 97 105 98 95 99 109 100 110 100 101 100 Develop an estimated linear regression equation showing how total points earned (y) is related to hours spent studying (x). What is the estimated linear regression model? (Round your numerical values to four decimal places.) ŷ = (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 fail to reject H0. We cannot 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. 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 fail to reject H0. We cannot conclude that there is a relationship between hours spent studying and total points earned.We reject H0. We can conclude that there is a relationship between hours spent studying and total points earned. We reject H0. We cannot conclude that there is a relationship between hours spent studying and total points earned.We fail to reject H0. We can conclude that there is a relationship between hours spent studying and total points earned. What are the correct interpretations of the estimated parameters? b0 is our estimate of the hours spent studying when total points earned is zero. b1 is our estimate of the change in hours spent studying for a one point increase in total points earned.b0 is our estimate of the change in total points earned for a one hour increase in time spent studying. b1 is our estimate of the total points earned when the hours spent studying is zero. b0 is our estimate of the change in hours spent studying for a one point increase in total points earned. b1 is our estimate of the hours spent studying when total points earned is zero.b0 is our estimate of the total points earned when the hours spent studying is zero. b1 is our estimate of the change in total points earned for a one hour increase in time spent studying. 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 total points earned (in %) does the model you estimated in part (b) explain? (Round your answer to two decimal places.) %

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 5PPS

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Question

Hours Spent Studying	Total Points Earned
22	12
20	18
29	25
24	25
43	28
46	29
39	35
40	39
51	40
43	43
39	43
51	49
52	50
65	51
57	53
56	53
52	55
66	55
63	57
68	57
67	59
42	59
65	59
69	60
72	60
66	61
53	61
45	61
58	62
81	62
60	62
57	62
77	62
78	63
67	64
78	64
72	64
58	64
71	65
76	65
79	66
83	66
65	66
72	66
71	66
52	67
78	67
70	67
81	67
80	68
79	68
72	68
75	68
91	68
65	68
84	69
77	69
78	70
72	70
84	70
83	70
67	70
80	71
78	71
72	72
70	72
94	72
92	72
84	73
98	73
78	73
78	73
84	73
74	74
90	74
83	74
84	74
83	75
78	75
93	75
80	75
101	76
81	76
83	76
91	76
83	76
93	76
78	76
78	77
65	77
84	77
97	77
88	77
93	78
93	78
95	78
95	79
91	79
95	79
94	79
95	80
102	80
105	80
83	80
99	80
97	81
79	81
101	81
88	82
93	83
95	85
94	85
104	85
88	85
80	86
98	86
83	86
91	86
90	87
83	87
92	88
88	88
99	89
101	90
101	90
99	90
102	90
84	90
110	91
93	91
105	91
109	91
91	92
104	92
95	92
98	92
91	93
104	93
104	94
106	95
95	95
106	95
92	95
101	96
95	96
109	96
95	96
101	96
105	97
104	97
104	97
105	98
95	99
109	100
110	100
101	100

Develop an estimated linear regression equation showing how total points earned (y) is related to hours spent studying (x). What is the estimated linear regression model? (Round your numerical values to four decimal places.)

ŷ =

(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 fail to reject H₀. We cannot 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.

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 fail to reject H₀. We cannot conclude that there is a relationship between hours spent studying and total points earned.We reject H₀. We can conclude that there is a relationship between hours spent studying and total points earned. We reject H₀. We cannot conclude that there is a relationship between hours spent studying and total points earned.We fail to reject H₀. We can conclude that there is a relationship between hours spent studying and total points earned.

What are the correct interpretations of the estimated parameters?

b₀ is our estimate of the hours spent studying when total points earned is zero. b₁ is our estimate of the change in hours spent studying for a one point increase in total points earned.b₀ is our estimate of the change in total points earned for a one hour increase in time spent studying. b₁ is our estimate of the total points earned when the hours spent studying is zero. b₀ is our estimate of the change in hours spent studying for a one point increase in total points earned. b₁ is our estimate of the hours spent studying when total points earned is zero.b₀ is our estimate of the total points earned when the hours spent studying is zero. b₁ is our estimate of the change in total points earned for a one hour increase in time spent studying.

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 total points earned (in %) does the model you estimated in part (b) explain? (Round your answer to two decimal places.)

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