A previous researcher has published a report demonstrating that students’ interest in studying mathematics is related to his or her interest in general academics. Furthermore, this researcher also claimed that interest in studying English-related subjects (literature, journalism, etc.) was not related to interest in mathematics. However, after reading the article, you believe the findings contradict your experience, and you believe there was a methodological flaw in the analysis. In particular, you believe it was necessary for the researcher to have accounted for another variable: gender.

Your plan is to collect a small data set from 2 groups of students. Your research questions are based around the hypothesis that the relationship between interest in mathematics and interest in both academics & English subjects is moderated by gender.

Using the same measurement scales for interest as the first researcher, you collect data from two groups. The first group is all boys. The second group is all girls. You will now run a multiple regression analysis using the interest in general academics and English classes as the independent variables and interest in mathematics as the dependent variable. For this analysis, you should use a significance level of α=0.05α=0.05.

GROUP-1
Boys GROUP-2
Girls

Interest in
General
Academics Interest in
English
Classes Interest in
Studying
Mathematics

43.4 49.9 41.2

54.5 52.7 46.6

55.9 42.1 38.5

35.9 56.2 62.2

57.7 52.9 50.3

61 63.2 55.5

56.7 50.2 50.2

45 58 40.4

29.7 54.3 49.6

36.4 28 32.3

33.6 46.7 30.2

53.6 42.8 27.3

42 63.1 55.6

46.1 38.4 38.3

24.8 45.5 33.8

61.2 60.5 55.5

50.7 32.9 35.5

50 65.5 42.1

56.3 54.2 42.4

27.7 57.8 45.3

Interest in
General
Academics Interest in
English
Classes Interest in
Studying
Mathematics

41.1 45.5 52.1

68.4 46.1 57.5

61.2 22.7 66.4

60.7 56.6 53

33.7 43.3 53.3

66.2 56.3 38.3

48.6 44.8 43.2

77.7 47.6 66.5

70.2 38 51.3

54.7 57 46.4

56.2 26.3 61.2

51.5 33.9 73.2

64.5 45.7 60.5

59.5 33.3 66.4

54.2 38.1 44.7

53.5 51.4 49.4

55 50 56.2

59.5 34.7 61.1

40.9 41 41.2

51.8 43.5 49.2

( 1a ) When examining the first group (boys), what is the estimated value for the influence (slope) of interest in general academics when predicting interest in mathematics (when running the regression include both interest in English classes and interest in general academics as the independent variables)?

( 2a ) Using the same regression output as above, what is the estimated value for the influence (slope) of interest in English classes when predicting interest in mathematics?

( 2b ) What is the p-value for this slope?

( 3a ) When examining the second group (girls), what is the estimated value for the influence (slope) of interest in general academics when predicting interest in mathematics (when running the regression include both interest in English classes and interest in general academics as the independent variables)?

( 3b ) What is the p-value for this slope?

( 4a ) Using the same regression output as above, what is the estimated value for the influence (slope) of interest in English classes when predicting interest in mathematics?

( 4b ) What is the p-value for this slope?
(Report answer accurate to 4 decimal places.)

Question

A previous researcher has published a report demonstrating that students’ interest in studying mathematics is related to his or her interest in general academics. Furthermore, this researcher also claimed that interest in studying English-related subjects (literature, journalism, etc.) was not related to interest in mathematics. However, after reading the article, you believe the findings contradict your experience, and you believe there was a methodological flaw in the analysis. In particular, you believe it was necessary for the researcher to have accounted for another variable: gender.

Your plan is to collect a small data set from 2 groups of students. Your research questions are based around the hypothesis that the relationship between interest in mathematics and interest in both academics & English subjects is moderated by gender.

Using the same measurement scales for interest as the first researcher, you collect data from two groups. The first group is all boys. The second group is all girls. You will now run a multiple regression analysis using the interest in general academics and English classes as the independent variables and interest in mathematics as the dependent variable. For this analysis, you should use a significance level of α=0.05α=0.05.

GROUP-1
Boys

GROUP-2
Girls

Interest in General Academics	Interest in English Classes	Interest in Studying Mathematics
43.4	49.9	41.2
54.5	52.7	46.6
55.9	42.1	38.5
35.9	56.2	62.2
57.7	52.9	50.3
61	63.2	55.5
56.7	50.2	50.2
45	58	40.4
29.7	54.3	49.6
36.4	28	32.3
33.6	46.7	30.2
53.6	42.8	27.3
42	63.1	55.6
46.1	38.4	38.3
24.8	45.5	33.8
61.2	60.5	55.5
50.7	32.9	35.5
50	65.5	42.1
56.3	54.2	42.4
27.7	57.8	45.3

Interest in General Academics	Interest in English Classes	Interest in Studying Mathematics
41.1	45.5	52.1
68.4	46.1	57.5
61.2	22.7	66.4
60.7	56.6	53
33.7	43.3	53.3
66.2	56.3	38.3
48.6	44.8	43.2
77.7	47.6	66.5
70.2	38	51.3
54.7	57	46.4
56.2	26.3	61.2
51.5	33.9	73.2
64.5	45.7	60.5
59.5	33.3	66.4
54.2	38.1	44.7
53.5	51.4	49.4
55	50	56.2
59.5	34.7	61.1
40.9	41	41.2
51.8	43.5	49.2

( 1a ) When examining the first group (boys), what is the estimated value for the influence (slope) of interest in general academics when predicting interest in mathematics (when running the regression include both interest in English classes and interest in general academics as the independent variables)?

( 2a ) Using the same regression output as above, what is the estimated value for the influence (slope) of interest in English classes when predicting interest in mathematics?

( 2b ) What is the p-value for this slope?

( 3a ) When examining the second group (girls), what is the estimated value for the influence (slope) of interest in general academics when predicting interest in mathematics (when running the regression include both interest in English classes and interest in general academics as the independent variables)?

( 3b ) What is the p-value for this slope?

( 4a ) Using the same regression output as above, what is the estimated value for the influence (slope) of interest in English classes when predicting interest in mathematics?

( 4b ) What is the p-value for this slope?
(Report answer accurate to 4 decimal places.)

Accepted Answer

Given Information:
Consider the given dataset:

Group-1 (Boys)
Group-2 (Girls)

Interest in…