Information about Correlation and Regression SPSS

Published on April 25, 2008

Author: edithosb

Source: slideshare.net

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

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 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)

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 .

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 .

Running Correlation in SPSS Strength – Direction - Significance Click Analyze – Correlate – Bivariate Move the two variables into the box – Click OK

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

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

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

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.

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

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

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

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.

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

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.

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.

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