You Are Given the Following Data, Where X₁ (Attendance Rate)Determine the Following Values: Intercept, B₁, B₂, SS_res, SS_reg, F

Question

Examlex · Accepted Answer

The Answer is Intercept = -36.536, b₁ = .869, b₂ = .036.

SS_re_g = 120.957, SS_re_s = 103.365, F(2,9) = 5.266 (p = .031, reject at .05), s²_res = 11.485.

s(b₁) = .764, s(b₂) = .014, t₁ = 1.138 (p = .285, fail to reject at .05), t₂ = 2.608 (p = .028, reject at .05).

Procedure:
Create a data set with three variables: Test (Y), Attend (X₁), and SAT (X₂). The data set should have 12 cases.

1) Go to Analyze

ightarrow

Regression

ightarrow

Linear.

2) Select Test to the Dependent list. Select Attend and SAT to the Independent(s) list.
"3) Click OK.

Selected SPSS Output:

ext { Model Summary }

\begin{array}{ccccc}\hline ext { Model } & R & R ext { Square } & ext { Adjusted } R ext { Square } & ext { Std. Error of the Estimate } \\hline 1 & .734^{a} & .539 & .437 & 3.3890 \\hline\end{array}

ext { a. Fredictors: (Constant), SAT, Attend }

ext { ANOVA }{ }^{\mathrm{b}}

\begin{array}{cccccc}\hline ext { Model } & ext { Sum of Squares } & d f & ext { Mean Square } & F & ext { Sig. } \\hline ext { Regression } & \mathbf{1 2 0 . 9 5 7} & 2 & 60.479 & \mathbf{5 . 2 6 6} & \mathbf{. 0 3 1}^{\mathbf{a}} \1 ext { Residual } & \mathbf{1 0 3 . 3 6 5} & 9 & \mathbf{1 1 . 4 8 5} & & \ ext { Total } & 224.323 & 11 & & &\\hline\end{array}

a. Fredictors: (Constant), SAT, Attend
b. Dependent Variable: Test $Intercept = -36.536, b1 = .869, b2 = .036. SSreg = 120.957, SSres = 103.365, F(2,9) = 5.266 (p = .031, reject at .05), s2res = 11.485. s(b1) = .764, s(b2) = .014, t1 = 1.138 (p = .285, fail to reject at .05), t2 = 2.608 (p = .028, reject at .05). Procedure: Create a data set with three variables: Test (Y), Attend (X1), and SAT (X2). The data set should have 12 cases. 1) Go to Analyze ightarrow Regression ightarrow Linear. 2) Select Test to the Dependent list. Select Attend and SAT to the Independent(s) list. 3) Click OK. Selected SPSS Output: ext { Model Summary } \begin{array}{ccccc} \hline ext { Model } & R & R ext { Square } & ext { Adjusted } R ext { Square } & ext { Std. Error of the Estimate } \ \hline 1 & .734^{a} & .539 & .437 & 3.3890 \ \hline \end{array} ext { a. Fredictors: (Constant), SAT, Attend } ext { ANOVA }{ }^{\mathrm{b}} \begin{array}{cccccc} \hline ext { Model } & ext { Sum of Squares } & d f & ext { Mean Square } & F & ext { Sig. } \ \hline ext { Regression } & \mathbf{1 2 0 . 9 5 7} & 2 & 60.479 & \mathbf{5 . 2 6 6} & \mathbf{. 0 3 1}^{\mathbf{a}} \ 1 ext { Residual } & \mathbf{1 0 3 . 3 6 5} & 9 & \mathbf{1 1 . 4 8 5} & & \ ext { Total } & 224.323 & 11 & & &\ \hline \end{array} a. Fredictors: (Constant), SAT, Attend b. Dependent Variable: Test Results: The results of the multiple linear regression suggest that a significant proportion of the total variation in graduation test scores was effectively predicted by attendance rate and SAT scores, F(2,9) = 5.266, p = .031. For Attend, the unstandardized partial slope (.869) and standardized partial slope (.268) are not statistically significantly different from 0 (t = 1.138, df = 9, p = .285). For SAT, the unstandardized partial slope (.036) and standardized partial slope (.614) are statistically significantly different from 0 (t = 2.608, df = 9, p = .028); with every point increase in SAT score, the graduation test score is expected to increase by .036 controlling for attendance rate. Multiple R2 indicates that 53.9% of the variation in graduation test scores was predicted by attendance rate and SAT score. This suggests a large effect size. The intercept was -36.536, which is not statistically significantly different from 0 at .05 level (t = -.529, df = 9, p = .609).$
Results:
The results of the multiple linear regression suggest that a significant proportion of the total variation in graduation test scores was effectively predicted by attendance rate and SAT scores, F(2,9) = 5.266, p = .031. For Attend, the unstandardized partial slope (.869) and standardized partial slope (.268) are not statistically significantly different from 0 (t = 1.138, df = 9, p = .285). For SAT, the unstandardized partial slope (.036) and standardized partial slope (.614) are statistically significantly different from 0 (t = 2.608, df = 9, p = .028); with every point increase in SAT score, the graduation test score is expected to increase by .036 controlling for attendance rate. Multiple R² indicates that 53.9% of the variation in graduation test scores was predicted by attendance rate and SAT score. This suggests a large effect size.

The intercept was -36.536, which is not statistically significantly different from 0 at .05 level (t = -.529, df = 9, p = .609)."

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