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Regression Analysis & Chi-square Test

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2. What information is provided by the numerical value of the Pearson correlation?

6. For the following scores, X Y
3 12
6 7
3 9
5 7
3 10

a. Compute the Pearson correlation. SP= ? Ssx= ? Ssy = ? r= ?

b. With a small sample, a single point can have a large effect on the magnitude of the correlation.
Change the score X = 5 to X = 0 and compute the Pearson Correlation again.
SP= ? Ssx= ? Ssy = ? r= ?

18. Sketch a graph showing the line for the equation Y = -2X + 4. On the same graph, show the line for Y = X - 4.

20. A set of n = 20 pairs of scores (X and Y values) has SSx = 25, SSy = 16, and SP = 12.5. If the mean for the X values is M = 6 and the mean for the Y values is M = 4.

a. Calculate the Pearson correlation for the scores. r= ?
b. Find the regression equation for predicting Y from the X values.
b= ? a= ? Y =

22. For the following scores, X Y
1 2
4 7
3 5
2 1
5 14
3 7

a. Find the regression equation for predicting Y from X
SP = ? SSx = ? a = ? b = ? Y = ?

b. Use the regression equation to find a predicted Y for each X.
X = 1, Y = X = 2, Y =
X = 4, Y = X = 5, Y =
X = 3, Y = X = 3, Y =

c. Find the difference between the actual Y value and the predicted Y value for each individual, square the differences, and add the squared values to obtain SSresidual.
SSresidual = ?

d. Calculate the Pearson correlation for these data. Use r2 and SSy to compute SSresidual
SP = ? SSx = ? SSy = ? r = ? r2 = ? SSresidual = ?

2. The student population at the state college consists of 55% females and 45% males.

a. The college theater department recently staged a production of a modern musical. A researcher recorded the gender of each student entering the theater and found a total of 385 females and 215 males. Is the gender distribution for theater goers significantly different from the distribution for the general college? Test at the 0.05 level of significance.

df = ? fe males = ? x2 males = ?
f0 = ? fe = females = ? x2 females = ?
x2 critical = ? x2 total = ?
Conclusion: ???

b. The same researcher also recorded the gender of each student watching a men's basketball game in the college gym and found a total of 83 females and 97 males. Is the gender distribution for basketball fans significantly different from the distribution for the general college? Test at the 0.05 level of significance.

df = ? fe males = ? x2 males = ?
f0 = ? fe = females = ? x2 females = ?
x2 critical = ? x2 total = ?
Conclusion: ???

4. Data from the Motor Vehicle Department indicate that 80% of all licensed drivers are older than age 25.

a. In a sample of n = 60 people who recently received speeding tickets, 38 were older than 25 years and the other 22 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use α = 0.05.
df = ? fe older= ? x2 older = ?
f0 = ? fe = younger = ? x2 younger = ?
x2 critical = ? x2 total = ?
Conclusion: ???

b. In a sample of n = 60 people who recently received parking tickets, 43 were older than 25 years and the other 17 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use α = 0.05.
df = ? fe older= ? x2 older = ?
f0 = ? fe = younger = ? x2 younger = ?
x2 critical = ? x2 total = ?
Conclusion: ???

# 6 Research has demonstrated that people tend to be attracted to others who are similar to themselves. One study demonstrated that individuals are disproportionately more likely to marry those with surnames that begin with the same last letter as their own (Jones, Pelham, Carvallo, & Mirenberg, 2004). The researchers began by looking at marriage records and recording the surname for each groom and the maiden name of each bride. From these records it is possible to calculate the probability of randomly matching a bride and a groom shoes last names begin with the same letter. Suppose that this probability is only 6.5%. Next, a sample of n = 200 married couples is selected and the number who shared the same last initial at the time they were married is counted. The resulting observed frequencies are as follows:
Same Initial Different Initial
19 181 200

Do these data indicate that the number of couples with the same last initial is significantly different that would be expected if couples were matched randomly? Test with α = 0.05.
df = ? fo = ? x2 critical = ?
fe = ? x2 calculated = ?
Conclusion : ???

8. A professor in the psychology department would like to determine whether there has been a significant change in grading practices over the years. It is known that the overall grade distribution for the department in 1985 has 14% As, 26% Bs, 31% Cs, 19% Ds, and 10% Fs. A sample of n = 200 psychology students from last semester produced the following grade distribution:
A B C D F
32 61 64 31 12

Do the data indicate a significant change in the grade distribution? Test at the 0.05 level of significance.
df = ? feA = ? x2 calculated A = ? x2 Total = ?
fo = ? feB = ? x2 calculated B = ? x2 critical = ?
feC = ? x2 calculated C = ?
feD = ? x2 calculated D = ?
feE = ? x2 calculated E = ?
Conclusion : ???

10. The color red is often associated with anger and male dominance. Based on this observation, Hill and Barton (2005) monitored the outcome of four combat sports (boxing, tae kwan do, Greco-Roman wrestling, and freestyle wrestling) during the 2004 Olympic games and found that participants wearing red outfits won significantly more than those wearing blue,
a. In 50 wrestling matches involving red versus blue, suppose that the red outfit won 31 times and lost 19 times. Is this result sufficient to conclude that red wins significantly more than would be expected by chance? Test at the 0.05 level of significance.
df = ? fo = ? x2 critical = ?
fe Red wins = ? x2 calculate = ?
Conclusion : ???

b. In 100 matches, suppose red won 62 times and lost 38. Is this sufficient to conclude that red wins significantly more than would be expected by chance? Again, use the α = 0.05.
df = ? fo = ? x2 critical = ?
fe Red wins = ? x2 calculate = ?
Conclusion : ???

c. Note that the winning percentage for red uniforms in part A is identical to the percentage in part b (31 out of 50 is 62%, and 62 out of 100 is also 62%). Although the two samples have identical winning percentages, one is significant and the other is not. Explain why the two samples lead to different conclusions.???

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Solution Summary

The solution provides a step by step method for the calculation of regression analysis. Formula for the calculation and interpretations of the results are also included.

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