Question

You may need to use the appropriate technology to answer this question. Multiple regression analysis was used to study how an individual's income (y in thousands of dollars) is influenced by age ($x_1$ in years), level of education ($x_2$ ranging from 1 to 5), and the individual's self- identified gender ($x_3$ where 0 = woman and 1 = man). The following is a partial result of a computer program that was used on a sample of 20 individuals. Coefficients Standard Error $x_1$ 0.629 0.092 $x_2$ 0.929 0.197 $x_3$ -0.517 0.927 ANOVA df SS MS F Regression 90 Residual 96 (a) Compute the multiple coefficient of determination. (Round your answer to four decimal places.) (b) Perform a $t$ test and determine whether the coefficient of the variable \"level of education\" (i.e., $x_2$) is significantly different from zero. Let $\alpha = 0.05$. State the null and alternative hypotheses. (Enter != for $\neq$ as needed.) $H_0$: $H_a$: Find the test statistic. (Round your answer to two decimal places.) Find the $p$-value. (Round your answer to four decimal places.) $p$-value = State your conclusion. $\circ$ Do not reject $H_0$. There is sufficient evidence to conclude that $\beta_2$ is significant. $\circ$ Do not reject $H_0$. There is insufficient evidence to conclude that $\beta_2$ is significant. $\circ$ Reject $H_0$. There is insufficient evidence to conclude that $\beta_2$ is significant. $\circ$ Reject $H_0$. There is sufficient evidence to conclude that $\beta_2$ is significant. (c) At $\alpha = 0.1$, perform an F test and determine whether the regression model is significant.

          You may need to use the appropriate technology to answer this question.
Multiple regression analysis was used to study how an individual's income (y in thousands of dollars) is influenced by age ($x_1$ in years), level of education ($x_2$ ranging from 1 to 5), and the individual's self-
identified gender ($x_3$ where 0 = woman and 1 = man). The following is a partial result of a computer program that was used on a sample of 20 individuals.
Coefficients	Standard Error
$x_1$	0.629	0.092
$x_2$	0.929	0.197
$x_3$	-0.517	0.927
ANOVA
df	SS	MS	F
Regression		90		
Residual		96	
(a) Compute the multiple coefficient of determination. (Round your answer to four decimal places.)
(b) Perform a $t$ test and determine whether the coefficient of the variable \"level of education\" (i.e., $x_2$) is significantly different from zero. Let $\alpha = 0.05$.
State the null and alternative hypotheses. (Enter != for $\neq$ as needed.)
$H_0$:
$H_a$:
Find the test statistic. (Round your answer to two decimal places.)
Find the $p$-value. (Round your answer to four decimal places.)
$p$-value =
State your conclusion.
$\circ$ Do not reject $H_0$. There is sufficient evidence to conclude that $\beta_2$ is significant.
$\circ$ Do not reject $H_0$. There is insufficient evidence to conclude that $\beta_2$ is significant.
$\circ$ Reject $H_0$. There is insufficient evidence to conclude that $\beta_2$ is significant.
$\circ$ Reject $H_0$. There is sufficient evidence to conclude that $\beta_2$ is significant.
(c) At $\alpha = 0.1$, perform an F test and determine whether the regression model is significant.

You may need to use the appropriate technology to answer this question.
Multiple regression analysis was used to study how an individual's income (y in thousands of dollars) is influenced by age (x1 in years), level of education (x2 ranging from 1 to 5), and the individual's self-
identified gender (x3 where 0 = woman and 1 = man). The following is a partial result of a computer program that was used on a sample of 20 individuals.
Coefficients Standard Error
x1 0.629 0.092
x2 0.929 0.197
x3 -0.517 0.927
ANOVA
df SS MS F
Regression 90
Residual 96
(a) Compute the multiple coefficient of determination. (Round your answer to four decimal places.)
(b) Perform a t test and determine whether the coefficient of the variable l̈evel of education(̈i.e., x2) is significantly different from zero. Let α = 0.05.
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:
Ha:
Find the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
∘ Do not reject H0. There is sufficient evidence to conclude that β2 is significant.
∘ Do not reject H0. There is insufficient evidence to conclude that β2 is significant.
∘ Reject H0. There is insufficient evidence to conclude that β2 is significant.
∘ Reject H0. There is sufficient evidence to conclude that β2 is significant.
(c) At α = 0.1, perform an F test and determine whether the regression model is significant.

Added by Fernando Y.

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