You are given the following data, where X₁ (high school cumulative GPA) and X₂ (having repeated grade; 0 = never repeated any grade and 1 = have repeated at least one grade; use 0 as the reference category) are used to predict Y (dropping out of high school, "1," vs. graduating high school, "0").
( $\alpha$ = .05)
$\begin{array}{ccc}\hline X_{\mathbf{1}} & X_{\mathbf{2}} & \boldsymbol{Y} \\\hline 2.50 & 1 & 0 \\2.60 & 0 & 0 \\2.75 & 0 & 0 \\1.33 & 1 & 1 \\3.00 & 1 & 0 \\3.42 & 0 & 0 \\2.70 & 1 & 1 \\2.33 & 1 & 1 \\1.75 & 0 & 1 \\2.80 & 0 & 0 \\\hline\end{array}$

Determine the following values based on simultaneous entry of the independent variables: -2LL, constant, b₁, b₂, se(b₁), se(b₂), odds ratios, Wald₁, Wald₂.

Question

You are given the following data, where X₁ (high school cumulative GPA) and X₂ (having repeated grade; 0 = never repeated any grade and 1 = have repeated at least one grade; use 0 as the reference category) are used to predict Y (dropping out of high school, "1," vs. graduating high school, "0").
(

\alpha

= .05)

\begin{array}{ccc}\hline X_{\mathbf{1}} & X_{\mathbf{2}} & \boldsymbol{Y} \\\hline 2.50 & 1 & 0 \\2.60 & 0 & 0 \\2.75 & 0 & 0 \\1.33 & 1 & 1 \\3.00 & 1 & 0 \\3.42 & 0 & 0 \\2.70 & 1 & 1 \\2.33 & 1 & 1 \\1.75 & 0 & 1 \\2.80 & 0 & 0 \\\hline\end{array}

Determine the following values based on simultaneous entry of the independent variables: -2LL, constant, b₁, b₂, se(b₁), se(b₂), odds ratios, Wald₁, Wald₂.

Quizplus · Accepted Answer

The Answer is -2LL = 5.048;
b₁₍_GPA₎ = ?6.617, b_2(Repeat) = 3.204, b_constant = 14.123;
se(b₁₍_GPA₎) = 4.308, se(b₂_(Repeat)) = 3.387;
odds ratio₁_(GPA) = .001, odds ratio_2(Repeat) = 24.631;
Wald₁₍_GPA₎ = 2.359, Wald₂_(Athletics) = .895.

Procedure:
Create a data set with three variables: GPA (X₁), Repeat (X₂), and Dropout (Y). The data set should have 10 cases.

Step 1: Go to Analyze

ightarrow

Regression

ightarrow

Binary Logistic.

Step 2: Select Dropout to the Dependent box. Select GPA and Repeat to the Covariate(s) list.

Step 3: Click Categorical. Move Repeat into the Categorical Covariates box. Select Reference Category: First. Click Change. Click Continue.

Step 4: Click Save. Check Probabilities and Group membership under Predicted Values. Check Standardized under Residuals. Check Cook's, Leverage values, and DfBeta(s) under Influences. Click Continue.

Step 5: Click Options. Check Classification plots, Hosmer-Lemeshow goodness-of -fit, Casewise listing of residuals, and CI for exp(B) under Statistics and Plots. Click Continue. Click OK.
Selected SPSS output:

\begin{array}{l} ext { Model Summary }\\begin{array}{cccc}\hline ext { Step } & -2 ext { Log likelihood } & ext { Cox \& Snell R Square } & ext { Nagelkerke R Square } \\hline 1 & 5.048^{\mathbf{a}} & .569 & .769 \\hline\end{array}\end{array}

\begin{array}{l} ext { Hosmer and Lemeshow Test }\\begin{array}{cccc}\hline ext { Step } & ext { Chi-square } & d f & ext { Sig. } \\hline 1 & 4.288 & 8 & .830 \\hline\end{array}\end{array}

\begin{array}{l} ext { Variables in the Equation }\\hline\begin{array}{r}\underline { 95 \% ext { C.I. for } \mathrm{EXP}(\mathrm{B})}\\begin{array}{cccccccccc}&& ext { B } & ext { S.E. } & ext { Wald } & d f & ext { Sig. } & \operatorname{Exp}(B)& ext { Lower }& ext { Upper } \\hline & ext { GPA } & -6.617 & \mathbf{4 . 3 0 8} & \mathbf{2 . 3 5 9} & 1 & .125 & \mathbf{0 0 1} & .000 & 6.209 \{ ext { Step }} & ext { Repeat(1) } & \mathbf{3 . 2 0 4} & \mathbf{3 . 3 8 7} & \mathbf{. 8 9 5} & 1 & .344 & \mathbf{2 4 . 6 3 1} & .032 & 18817.875 \1^{1}& ext { Constant } & \mathbf{1 4 . 1 2 3} & 9.936 & 2.020 & 1 & .155 & 1359604.313 & & \\hline\end{array}\end{array}\end{array}

ext { a. Variable(s) entered on step 1: GPA, Repeat. }

You Are Given the Following Data, Where X1 (High School α\alphaα

You Are Given the Following Data, Where X₁ (High School $\alpha$