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# Correlation and Regression SPSS

## on Apr 24, 2008

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Directions for running correlation, regression, and scatterplots in SPSS.

Directions for running correlation, regression, and scatterplots in SPSS.

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## Correlation and Regression SPSSPresentation Transcript

• Correlation Scatterplots Regression Generating results in SPSS Reading SPSS output
• Correlation, Scatterplots and Regression
• Correlation measures the strength and the direction of relationship
• Scatterplots present visual image of data
• Regression produces a best-fit line to predict dependent variable from independent variable
• Significance of relationship tested with correlation or regression
• Correlation: Linear Relationship s Strong relationship = good linear fit Very good fit Moderate fit Points clustered closely around a line show a strong correlation. The line is a good predictor (good fit) with the data. The more spread out the points, the weaker the correlation, and the less good the fit. The line is a REGRESSSION line (Y = bX + a) View slide
• Interpreting Correlation Coefficient r
• strong correlation: r > .70 or r < – .70
• moderate correlation: r is between .30 & .70 or r is between – .30 and – .70
• weak correlation: r is between 0 and .30 or r is between 0 and – .30 .
View slide
• Running Correlation in SPSS Strength – Direction - Significance
• Click Analyze – Correlate – Bivariate
• Move the two variables into the box – Click OK
• SPSS Correlation Output
• Value of Correlation Coefficient on first line r = +.173
• Relationship is positive
• Relationship is weak
• p- value (Significance) is on the second line p < .001 (whenever SPSS shows .000)
• Relationship is significant
• Reject H 0
• Correlation for Your Project
• Your dependent variable is Interval/Ratio
• Look at the data set and select one other interval/ratio variable that might be related to (predictive of) your dependent variable
• Following the instructions above
• run correlation of that variable.
• run scatterplot of the variable
• GENERATE A SCATTERPLOT TO SEE THE RELATIONSHIPS Go to Graphs -> Legacy dialogues -> Scatter -> Simple Click on DEPENDENT V. and move it to the Y-Axis Click on the OTHER V. and move it to the X-Axis Click OK
• Scatterplot might not look promising at first Double click on chart to open a CHART EDIT window
• use Options -> Bin Element Simply CLOSE this box. Bins are applied automatically.
• BINS Dot size now shows number of cases with each pair of X, Y values DO NOT CLOSE CHART EDITOR YET!
• Add Fit Line (Regression)
• In Chart Editor:
• Elements ->Fit Line at Total
• Close dialog box that opens
• Close Chart Editor window
• Edited Scatterplot
• Distribution of cases shown by dots (bins)
• Trend shown by fit line.
• Regression
• Regression predicts the Dependent Variable based on the Independent Variable
• Computes best-fit line for prediction
• Output includes slope and intercept for line
• Hypothesis Test based on ANOVA
• SS total computed
• SS total divided into Regression (predicted) and Error (random)
• Effect size = R 2 for regression
• SPSS for Regression
• Analyze ->Regression ->Linear
• Simple Linear Regression (One independent variable)
• Move Dependent Variable into box marked “Dependent”
• Move Independent Variable into box marked “Independent”
• Click OK
• Regression Output Each element of output considered separately in the following slides.
• ANOVA Table
• Regression SS refers to variability related to the Independent Variable – the treatment
• Residual SS refers to variability not related to the Independent Variable – the error or chance element.
• For regression, df for treatment is 1 per variable
• Compute MS and F in the same way as ANOVA
• If p -value (Sig) < α the Regression line fits the data better than a flat line; the relationship is significant.
• The Regression Line Equation
• Y = bX + a
• b is the coefficient for the Independent Variable
• a is the constant coefficient (intercept)
• Predict values of Y based on values of X
• Effect Size: R 2
• In regression, the effect size is similar to η 2 in ANOVA
• SS regression /SS total
• Represented by R 2 (capital R )
• For simple regression (one variable) use the R-Square figure.
• Sample Write-Up Data from the 2004 General Social Survey were used to explore the relationship between age and income, as most Americans expect to earn more money after years in the workforce. Respondents’ age showed a weak positive correlation ( r = .173, p < .001) with income level. Linear regression demonstrated a significant positive relationship ( F (1,1796) = 55.359, p < .001). Income increased approximately one-third of an income level for each increased decade of age ( b = .037). Due to the large range of income levels at every age (see Figure 1 ), age only accounts for 3% of the variability of income levels. Older people do tend to earn higher incomes, but other characteristics are probably a better predictor of income than age.