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4. Calculate SP (the sum of products of deviations) for the following scores. NOTE both means are decimal values, so the computational formula works well.
X Y
0 2
0 1
1 0
2 1
1 2
0 3
12. Judge and Cable (2010) report the results of a study demonstrating a negative relationship between weight and income for a group of women professionals. Following are data similar to those obtained in the study. To simplify the weight variable, the women are classified into five categories that measure actual weight relative to height, from 1=thinnest to 5= heaviest. Income figures are annual income in thousands rounded to the nearest $1,000.
A. calculate the Pearson correlation for these data
B. is the correlation statistically significant? Use a two tailed test with ? = .05
WEIGHT X INCOME Y
1 125
2 78
4 49
3 63
5 35
2 84
5 38
3 51
1 93
4 44
24. Studies have shown that people with high intelligence are generally more likely to volunteer as participants in research but not for research that involves unusual experiences such as hypnosis. To examine this phenomenon a researcher administers a questionnaire to a sample of college students. The survey asks for the students grade point average as a measure of intelligence and whether the students would like to take part in a future study in which participants would be hypnotized. The results showed that 7 of the 10 lower intelligence people were willing to participate but only 2 of 10 higher intelligence people were willing.
a. convert the data to a form suitable for computing the phi-coefficient. Code the two intelligence categories as 0 and 1 for the X variable, and code the willingness to participate as 0 and 1 for the Y variable.
b. Compute the phi- coefficient for the data.
PART 2
10. For the following scores:
a. find the regression equation or predicting Y from X
b. Calculate the predicted Y value for each X
18. For the following data:
a. find the regression equation for predicting Y from X
b. use the regression equation to find a predicted Y for each X.
c. Find the differences between the actual Y value and the predicted Y value for each individual, square the differences, and add the square values to obtain the SS residual.
d. calculate the Pearson correlation for these data. Use r2 and SSy to compute SS residual with equation 16.11 you should obtain the same value as in part c.
x y
7 16
5 2
6 1
3 2
4 9
20. A researcher obtained to following multiple-regression equation using two predictor variables: Y=0.5X1+4.5X2+9.6. given that SSy=210, the SP value for X1 and Y is 40 and the SP value for X2 and Y is 9, find R2 the percentage of variance accounted for by the equation.
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