Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 95 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 210 The estimated regression equation for these data is ŷ = −17.17 + 1.99x1 + 4.71x2. Here, SST = 14,950.9, SSR = 13,830.2, sb1 = 0.2460, and sb2 = 0.9442. (a) Test for a significant relationship among x1, x2, and y.Use ? = 0.05. State the null and alternative hypotheses. -H0: ?1 < ?2 Ha: ?1 ≥ ?2 -H0: ?1 = ?2 = 0 Ha: One or more of the parameters is not equal to zero. -H0: ?1 > ?2 Ha: ?1 ≤ ?2 -H0: ?1 ≠ 0 and ?2 = 0 Ha: ?1 = 0 and ?2 ≠ 0 -H0: ?1 ≠ 0 and ?2 ≠ 0 Ha: One or more of the parameters is equal to zero. Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables. -Do not reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables. -Reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables. -Do not reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables. (b) Is ?1 significant? Use ? = 0.05. State the null and alternative hypotheses. -H0: ?1 < 0 Ha: ?1 ≥ 0 -H0: ?1 ≠ 0 Ha: ?1 = 0 -H0: ?1 > 0 Ha: ?1 ≤ 0 -H0: ?1 = 0 Ha: ?1 > 0 -H0: ?1 = 0 Ha: ?1 ≠ 0 Find the value of the test statistic. (Round your answer to two decimal places.) statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is insufficient evidence to conclude that ?1 is significant. -Reject H0. There is insufficient evidence to conclude that ?1 is significant. - Do not reject H0. There is sufficient evidence to conclude that ?1 is significant. -Reject H0. There is sufficient evidence to conclude that ?1 is significant. (c) Is ?2 significant? Use ? = 0.05. State the null and alternative hypotheses. -H0: ?2 > 0 Ha: ?2 ≤ 0 -H0: ?2 ≠ 0 Ha: ?2 = 0 -H0: ?2 < 0 Ha: ?2 ≥ 0 -H0: ?2 = 0 Ha: ?2 > 0 -H0: ?2 = 0 Ha: ?2 ≠ 0. Find the value of the test statistic. (Round your answer to two decimal places.) statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is sufficient evidence to conclude that ?2 is significant. -Reject H0. There is sufficient evidence to conclude that ?2 is significant. - Do not reject H0. There is insufficient evidence to conclude that ?2 is significant. -Reject H0. There is insufficient evidence to conclude that ?2 is significant.

Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 95 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 210 The estimated regression equation for these data is ŷ = −17.17 + 1.99x1 + 4.71x2. Here, SST = 14,950.9, SSR = 13,830.2, sb1 = 0.2460, and sb2 = 0.9442. (a) Test for a significant relationship among x1, x2, and y.Use ? = 0.05. State the null and alternative hypotheses. -H0: ?1 < ?2 Ha: ?1 ≥ ?2 -H0: ?1 = ?2 = 0 Ha: One or more of the parameters is not equal to zero. -H0: ?1 > ?2 Ha: ?1 ≤ ?2 -H0: ?1 ≠ 0 and ?2 = 0 Ha: ?1 = 0 and ?2 ≠ 0 -H0: ?1 ≠ 0 and ?2 ≠ 0 Ha: One or more of the parameters is equal to zero. Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables. -Do not reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables. -Reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables. -Do not reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables. (b) Is ?1 significant? Use ? = 0.05. State the null and alternative hypotheses. -H0: ?1 < 0 Ha: ?1 ≥ 0 -H0: ?1 ≠ 0 Ha: ?1 = 0 -H0: ?1 > 0 Ha: ?1 ≤ 0 -H0: ?1 = 0 Ha: ?1 > 0 -H0: ?1 = 0 Ha: ?1 ≠ 0 Find the value of the test statistic. (Round your answer to two decimal places.) statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is insufficient evidence to conclude that ?1 is significant. -Reject H0. There is insufficient evidence to conclude that ?1 is significant. - Do not reject H0. There is sufficient evidence to conclude that ?1 is significant. -Reject H0. There is sufficient evidence to conclude that ?1 is significant. (c) Is ?2 significant? Use ? = 0.05. State the null and alternative hypotheses. -H0: ?2 > 0 Ha: ?2 ≤ 0 -H0: ?2 ≠ 0 Ha: ?2 = 0 -H0: ?2 < 0 Ha: ?2 ≥ 0 -H0: ?2 = 0 Ha: ?2 > 0 -H0: ?2 = 0 Ha: ?2 ≠ 0. Find the value of the test statistic. (Round your answer to two decimal places.) statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is sufficient evidence to conclude that ?2 is significant. -Reject H0. There is sufficient evidence to conclude that ?2 is significant. - Do not reject H0. There is insufficient evidence to conclude that ?2 is significant. -Reject H0. There is insufficient evidence to conclude that ?2 is significant.

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 22PFA

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Related questions

Question

Consider the following data for a dependent variable y and two independent variables,

x₁

and

x₂.

x₁	x₂	y
30	12	95
47	10	108
25	17	112
51	16	178
40	5	94
51	19	175
74	7	170
36	12	117
59	13	142
76	16	210

The estimated regression equation for these data is

ŷ = −17.17 + 1.99x₁ + 4.71x₂.

Here, SST = 14,950.9, SSR = 13,830.2,

s_b1 = 0.2460,

and

s_b2 = 0.9442.

(a)

Test for a significant relationship among x₁, x₂, and y.Use ? = 0.05.

State the null and alternative hypotheses.

-H₀: ?₁ < ?₂
H_a: ?₁ ≥ ?₂

-H₀: ?₁ = ?₂ = 0
H_a: One or more of the parameters is not equal to zero.

-H₀: ?₁ > ?₂
H_a: ?₁ ≤ ?₂

-H₀: ?₁ ≠ 0 and ?₂ = 0
H_a: ?₁ = 0 and ?₂ ≠ 0

-H₀: ?₁ ≠ 0 and ?₂ ≠ 0
H_a: One or more of the parameters is equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Statistic=??

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

p-value = ??

State your conclusion.

-Reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.

-Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.

-Reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.

-Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.

(b)

Is ?₁ significant? Use ? = 0.05.

State the null and alternative hypotheses.

-H₀: ?₁ < 0
H_a: ?₁ ≥ 0

-H₀: ?₁ ≠ 0
H_a: ?₁ = 0

-H₀: ?₁ > 0
H_a: ?₁ ≤ 0

-H₀: ?₁ = 0
H_a: ?₁ > 0

-H₀: ?₁ = 0
H_a: ?₁ ≠ 0

Find the value of the test statistic. (Round your answer to two decimal places.)

statistic=??

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

p-value = ??

State your conclusion.

-Do not reject H₀. There is insufficient evidence to conclude that ?₁ is significant.

-Reject H₀. There is insufficient evidence to conclude that ?₁ is significant.

- Do not reject H₀. There is sufficient evidence to conclude that ?₁ is significant.

-Reject H₀. There is sufficient evidence to conclude that ?₁ is significant.

(c)

Is ?₂ significant? Use ? = 0.05.

State the null and alternative hypotheses.

-H₀: ?₂ > 0
H_a: ?₂ ≤ 0

-H₀: ?₂ ≠ 0
H_a: ?₂ = 0

-H₀: ?₂ < 0
H_a: ?₂ ≥ 0

-H₀: ?₂ = 0
H_a: ?₂ > 0

-H₀: ?₂ = 0
H_a: ?₂ ≠ 0.

Find the value of the test statistic. (Round your answer to two decimal places.)

statistic=??

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

p-value = ??

State your conclusion.

-Do not reject H₀. There is sufficient evidence to conclude that ?₂ is significant.

-Reject H₀. There is sufficient evidence to conclude that ?₂ is significant.

- Do not reject H₀. There is insufficient evidence to conclude that ?₂ is significant.

-Reject H₀. There is insufficient evidence to conclude that ?₂ is significant.

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x₁	x₂	y
30	12	95
47	10	108
25	17	112
51	16	178
40	5	94
51	19	175
74	7	170
36	12	117
59	13	142
76	16	210

x₁	x₂	y
30	12	95
47	10	108
25	17	112
51	16	178
40	5	94
51	19	175
74	7	170
36	12	117
59	13	142
76	16	210

x₁	x₂	y
30	12	95
47	10	108
25	17	112
51	16	178
40	5	94
51	19	175
74	7	170
36	12	117
59	13	142
76	16	210