You are given the following data, where X₁ (Pretest score) and X₂ (Hours spent in the program) are used to predict Y (Posttest score):

$\begin{array}{ccc}\hline \boldsymbol{Y} & \boldsymbol{X}_{\mathbf{1}} & \boldsymbol{X}_{\mathbf{2}} \\\hline 65 & 60 & 7.5 \\82 & 62 & 9.0 \\94 & 75 & 8.5 \\80 & 78 & 7.0 \\87 & 65 & 10.0 \\66 & 60 & 8.0 \\\hline\end{array}$
Determine the following values: intercept, b₁, b₂, SS_res, SS_reg, F, s_res², s(b₁), s(b₂), t₁, t₂.

Question

You are given the following data, where X₁ (Pretest score) and X₂ (Hours spent in the program) are used to predict Y (Posttest score):

\begin{array}{ccc}\hline \boldsymbol{Y} & \boldsymbol{X}_{\mathbf{1}} & \boldsymbol{X}_{\mathbf{2}} \\\hline 65 & 60 & 7.5 \\82 & 62 & 9.0 \\94 & 75 & 8.5 \\80 & 78 & 7.0 \\87 & 65 & 10.0 \\66 & 60 & 8.0 \\\hline\end{array}

Determine the following values: intercept, b₁, b₂, SS_res, SS_reg, F, s_res², s(b₁), s(b₂), t₁, t₂.

Quizplus · Accepted Answer

The Answer is Intercept = -70.662, b₁ = 1.235, b₂ = 8.077.

SS_re_g = 619.504, SS_re_s = 44.496, F(2,3) = 20.884 (p < .017, reject at .05), s²_res = 14.832.

s(b₁) = .227, s(b₂) = 1.660, t₁ = 5.437 (p = .012, reject at .05), t₂ = 4.866 (p = .017, reject at .05).

Procedure:
Create a data set with three variables: Posttest (Y), Pretest (X₁), and Hour (X₂). The data set should have six cases.

1) Go to Analyze

ightarrow

Regression

ightarrow

Linear.

2) Select Posttest to the Dependent list. Select Pretest and Hour to the Independent(s) list.

"3) Click OK.
Selected SPSS Output:

ext { Model Summary }

\begin{array}{ccccc}\hline ext { Model } & R & R S q u a r e & ext { Adjusted } R ext { Square } & ext { Std. Error of the Estimate } \\hline 1 & .966^{2} & .933 & .888 & 3.851 \\hline\end{array}

ext { a. Fredictors: (Constant), Hour, Pretest }

{ANOVA}^{b}

\begin{array}{ccccccc}\hline { ext { Model }} & ext { Sum of Squares } & d f & ext { Mean Square } & F & ext { Sig. } \\hline {\begin{array}{c} ext { Regression }\end{array}} & \mathbf{6 1 9 . 5 0 4} & 2 & 309.752 & \mathbf{2 0 . 8 8 4} & \mathbf{. 0 1 7}^a \1 ext { Residual } & \mathbf{4 4 . 4 9 6} & 3 & \mathbf{1 4 . 8 3 2} & &\ ext { Total }&664.000&5\\hline\end{array}

a. Predictors: (Constant), Hour, Fretest
b. Dependent Variable: Posttest Results:
$Intercept = -70.662, b1 = 1.235, b2 = 8.077. SSreg = 619.504, SSres = 44.496, F(2,3) = 20.884 (p < .017, reject at .05), s2res = 14.832. s(b1) = .227, s(b2) = 1.660, t1 = 5.437 (p = .012, reject at .05), t2 = 4.866 (p = .017, reject at .05). Procedure: Create a data set with three variables: Posttest (Y), Pretest (X1), and Hour (X2). The data set should have six cases. 1) Go to Analyze ightarrow Regression ightarrow Linear. 2) Select Posttest to the Dependent list. Select Pretest and Hour to the Independent(s) list. 3) Click OK. Selected SPSS Output: ext { Model Summary } \begin{array}{ccccc} \hline ext { Model } & R & R S q u a r e & ext { Adjusted } R ext { Square } & ext { Std. Error of the Estimate } \ \hline 1 & .966^{2} & .933 & .888 & 3.851 \ \hline \end{array} ext { a. Fredictors: (Constant), Hour, Pretest } {ANOVA}^{b} \begin{array}{ccccccc} \hline { ext { Model }} & ext { Sum of Squares } & d f & ext { Mean Square } & F & ext { Sig. } \ \hline {\begin{array}{c} ext { Regression } \end{array}} & \mathbf{6 1 9 . 5 0 4} & 2 & 309.752 & \mathbf{2 0 . 8 8 4} & \mathbf{. 0 1 7}^a \ 1 ext { Residual } & \mathbf{4 4 . 4 9 6} & 3 & \mathbf{1 4 . 8 3 2} & &\ ext { Total }&664.000&5\ \hline \end{array} a. Predictors: (Constant), Hour, Fretest b. Dependent Variable: Posttest Results: The results of the multiple linear regression suggest that a significant proportion of the total variation in posttest scores was effectively predicted by pretest scores and hours spent in the program, F(2,3) = 20.884, p = .017. For Pretest, the unstandardized partial slope (1.235) and standardized partial slope (.846) are statistically significantly different from 0 (t = 5.437, df = 3, p = .012); with every one-point increase in pretest, posttest score will increase by 1.235 when controlling for Hour. For Hour, the unstandardized partial slope (8.077) and standardized partial slope (.757) are statistically significantly different from 0 (t = 4.866, df = 3, p = .017); with every additional hour spent in the program, posttest score is expected to increase by 8.077 when controlling for Pretest scores. Thus, Pretest and Hour were shown to be statistically significant predictors of Posttest, both individually and collectively. Multiple R2 indicates that 93.3% of the variation in Salary was predicted by Pretest and Hour. This suggests a large effect size. The intercept was -70.662, which is not statistically significantly different from 0 at the .05 level (t = -3.042, df = 3, p = .056).$
The results of the multiple linear regression suggest that a significant proportion of the total variation in posttest scores was effectively predicted by pretest scores and hours spent in the program, F(2,3) = 20.884, p = .017. For Pretest, the unstandardized partial slope (1.235) and standardized partial slope (.846) are statistically significantly different from 0 (t = 5.437, df = 3, p = .012); with every one-point increase in pretest, posttest score will increase by 1.235 when controlling for Hour. For Hour, the unstandardized partial slope (8.077) and standardized partial slope (.757) are statistically significantly different from 0 (t = 4.866, df = 3, p = .017); with every additional hour spent in the program, posttest score is expected to increase by 8.077 when controlling for Pretest scores. Thus, Pretest and Hour were shown to be statistically significant predictors of Posttest, both individually and collectively. Multiple R² indicates that 93.3% of the variation in Salary was predicted by Pretest and Hour. This suggests a large effect size.

The intercept was -70.662, which is not statistically significantly different from 0 at the .05 level (t = -3.042, df = 3, p = .056)."

You Are Given the Following Data, Where X1 (Pretest Score)

You Are Given the Following Data, Where X₁ (Pretest Score)