Illustrated Example
Multiple Regression

This example comes from the Steven's text on page 262. A researcher wants to investigate what predictors (or explains) instructors' evaluations. From previous research the researcher identifies 5 variables that he considers important in predicting instructors' evaluations: (a) clarity, (b) stimulation, (c) knowledge, (d) interest, and (e) course evaluation. 

Podcast -- [Standard Multiple Regression -- SPSS~12 mins]

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SPSS Analysis

Move dependent variable and independent variables to the appropriate box

Go under the Statistics... option and check the part and partial correlations (this is going to give us something similar to the effect sizes were have used in previous analyses)

SPSS Output

 

Results

    A standard multiple regression was conducted to predict instructors' evaluation from (a) clarity, (b) stimulation, (c) knowledge, (d) interest, and (e) course evaluation. Analysis was performed using SPSS REGRESSION.

    Before conducting the multiple regression, the data were screened for missing data, outliers, and assumptions. There were no missing values and no univariate or multivariate outliers detected. The means, standard deviations, skewness, and kurtosis for the variables are reported in Table 2. An examination of the skewness values and a visual inspection frequency distributions suggested that the distributions of all the variables were approximately normally distributed. Examination of bivariate scatterplots indicate that there were linear relationships between all the variables. The correlation coefficients among the variables are reported in Table 3.

    The unstandardized regression coefficients (B) and intercept, the standardized regression coefficients (β), and semipartial correlations (sri) are reported in Table 4. The variance accounted for (R2 ) equaled .89 (adjusted R2 = .87), which was significantly different from zero (F=44.00, p<.01). Four of the five independent variables (or predictor variables) contributed significantly to the prediction of instructors evaluation, Clarity, Stimulation, Knowledge, and Course Evaluation. Clarity had the largest positive standardized beta and semipartial correlation coefficient. Stimulation, Course Evaluation, and Knowledge had similar positive standardized betas and semipartial correlation coefficients. While Interest was hypothesized to be positively related to instructor's evaluation, it was not statistically significant and the standardized beta and semipartial correlation coefficient were virtually zero.

Table 4

Unstandardized Regression Coefficients (B) and Intercept, the Standardized Regression Coefficients (β), Semipartial Correlations (sri), t-values, and p-values  

IV s

B

β

sri

t-value

p-value

Intercept

-.44

 

 

-1.89

.07

Clarity

.39

.52

.34

5.41

<.01

Stimulation

.20

.27

.20

3.19

<.01

Knowledge

.28

.21

.16

2.56

.02

Interest

.01

.01

.01

.11

.91

Course Eval

.27

.24

.16

2.46

.02