SPSS Analysis and Tasks
1
Regression One Predictor
Descriptive Statistics
Mean
ExamTotPer
Std. Deviation
N
76.4236
9.79472
124
5.90
3.199
124
PreTotal
Correlations
ExamTotPer
ExamTotPer
PreTotal
1.000
.475
.475
1.000
.
.000
PreTotal
.000
.
ExamTotPer
124
124
PreTotal
124
124
Pearson Correlation
PreTotal
ExamTotPer
Sig. (1-tailed)
N
Model Summary
Model
R
R Square
Adjusted R
Std. Error of the
Square
Estimate
Change Statistics
R Square
F Change
df1
Change
1
.475a
.226
.219
8.65407
.226
35.561
1
Model Summary
Model
Change Statistics
df2
1
a. Predictors: (Constant), PreTotal
Sig. F Change
122a
.000
SPSS Analysis and Tasks
ANOVAa
Model
1
Sum of Squares
df
Mean Square
Regression
2663.264
1
2663.264
Residual
9136.928
122
74.893
11800.192
123
Total
F
Sig.
35.561
.000b
a. Dependent Variable: ExamTotPer
b. Predictors: (Constant), PreTotal
Coefficientsa
Model
Unstandardized Coefficients
Standardized
t
Sig.
Coefficients
B
(Constant)
Std. Error
67.837
1.636
1.455
.244
Beta
41.460
.000
5.963
.000
1
PreTotal
a. Dependent Variable: ExamTotPer
.475
2
SPSS Analysis and Tasks
3
Regression Two Predictors
Descriptive Statistics
Mean
ExamTotPer
Std. Deviation
N
76.4236
9.79472
124
5.90
3.199
124
-13.00
26.024
124
PreTotal
AbilDis
Correlations
ExamTotPer
ExamTotPer
Pearson Correlation
N
AbilDis
1.000
.475
.283
PreTotal
.475
1.000
.137
AbilDis
.283
.137
1.000
.
.000
.001
PreTotal
.000
.
.065
AbilDis
.001
.065
.
ExamTotPer
124
124
124
PreTotal
124
124
124
AbilDis
124
124
124
ExamTotPer
Sig. (1-tailed)
PreTotal
Model Summary
Model
1
R
.523a
R Square
.274
Adjusted R
Std. Error of the
Square
Estimate
.262
Change Statistics
R Square Change
8.41475
.274
F Change
df1
df2
Sig. F Change
22.825
2
121
.000
a. Predictors: (Constant), AbilDis, PreTotal
ANOVAa
Model
1
Sum of Squares
df
Mean Square
Regression
3232.430
2
1616.215
Residual
8567.762
121
70.808
11800.192
123
Total
a. Dependent Variable: ExamTotPer
b. Predictors: (Constant), AbilDis, PreTotal
F
22.825
Sig.
.000b
SPSS Analysis and Tasks
4
Coefficientsa
Model
Unstandardized Coefficients
Standardized
t
Sig.
Coefficients
B
(Constant)
1
PreTotal
AbilDis
Std. Error
69.471
1.692
1.362
.239
.083
.029
Beta
41.056
.000
.445
5.687
.000
.222
2.835
.005
a. Dependent Variable: ExamTotPer
Tasks:
1. Use the data from the Excel spreadsheet to demonstrate multiple regression. Note that
each individual has a Y score and two X scores that are used as predictor variables.
a. Compute the SS values for Y and for both of the X scores, as well as all of the SP
values.
b. Use these values to compute the coefficients, b1; AbilDis and b2; PreTotal and the
constant, a, for the regression equation.
𝑌̂ = 𝑏1 𝑋1 + 𝑏2 𝑋2 + 𝑎
2. Percentage of Variance Accounted For and Residual Variance
a. For a regression equation with two predictor variables, use the following equation
to compute R2
𝑅2 =
𝑏1 𝑆𝑃𝑋1𝑌 + 𝑏2 𝑆𝑃𝑋2𝑌
𝑆𝑆𝑌
b. Compute R 2 and 1 – R 2 from the residuals
i. The value of R 2 can also be obtained indirectly, by computing the residual,
or difference between the predicted Y and the actual Y for each individual,
then computing the sum of the squared residuals.
ii. Explain and interpret your findings. Your explanation should not just be
what you are doing but how these specific calculations are used to explain
common variance; that is, model based on the relationship versus model
based on no relationship.
3. Compute and interpret the standard error of estimate
a. The standard error of estimate = √𝑀𝑆𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
SPSS Analysis and Tasks
5
4. Test the significance of the multiple regression equation by calculating values in an
ANOVA source table.
a. Explain each of the values in the ANOVA source table under the headings: Source,
SS, df, MS, Fobs, Fcrit.
b. Interpret findings from the ANOVA source table.
5. Evaluate the contribution of each predictor variable
a. Compute the correlation between X1-PreTotal and YExamTotal
𝑟=
𝑆𝑃𝑋1𝑌
√(𝑆𝑆𝑋1 )(𝑆𝑆𝑌 )
b. r2 means that the relationship with X1 predicts some percentage of the variance for
the Y scores.
c. I will add a video to review this process.
6. Interpret the results of the analysis.
a. Do findings from the analysis support the notion that pretesting impacts on exam
performance?
b. How does adding of a second variable, ability discrepancy, extend the findings
from the analysis?