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: school year.

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 school year.

Using the same measurement scales for interest as the first researcher, you collect data from two groups. The first group is all year-8 students. The second group is all year-10 students. 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=0.02α=0.02.

GROUP-1 Year-8 Students	GROUP-2 Year-10 Students
Interest in General Academics Interest in English Classes Interest in Studying Mathematics 54.7 68.9 56.5 52.2 52.8 31.2 53.5 40.4 23.2 44.6 49.5 46 52.4 35 38.5 54.3 51.7 36.9 51.2 51.9 47.9 51.9 55.9 35.1 48.3 61.5 46 55.3 47.7 38.6 47.4 53.5 27 51 62.3 38.9 34.4 27.2 24.8 68 39.1 38.9 53.1 74.5 40.7 43.6 44.8 34.2 53.4 69.4 44.5 63.3 59.1 44.4 68 38 40.4 44.2 44 36.9	Interest in General Academics Interest in English Classes Interest in Studying Mathematics 52.7 50 48.9 58.1 45.9 58.3 71.6 54.8 33.6 65.2 48.2 35.2 78.1 49.4 50.8 65.7 67 41.6 46.5 51.2 49.3 63.2 44.7 56.5 68 49.7 51.2 66.6 36.2 47.3 64 31.4 56.4 52.2 38.3 54.9 67.2 57 37.4 47.3 44.8 49 69.1 51.7 49.3 50.8 42 47.4 67.3 44.7 55 75 24.4 66.9 58.3 60.3 45.5 58.7 53 44.7

( 1a ) When examining the first group (year-8), what is the estimated value for the influence of interest in general academics on interest in mathematics (after accounting for interest in English classes)?

(Report answer accurate to 3 decimal places.)

( 1b ) What is the p-value for this slope?   
(Report answer accurate to 4 decimal places.)

( 1c ) For the year-8 group, is the influence of interest in general academics on interest in mathematics statistically significantly different from zero?

• yes
• no

( 2a ) When examining the first group (year-8), what is the estimated value for the influence of interest in English classes on interest in mathematics (after accounting for interest in general academics)?

(Report answer accurate to 3 decimal places.)

( 2b ) What is the p-value for this slope?   
(Report answer accurate to 4 decimal places.)

( 2c ) For the year-8 group, is the influence of interest in English classes on interest in mathematics statistically significantly different from zero?

• yes
• no

( 3a ) When examining the second group (year-10), what is the estimated value for the influence of interest in general academics on interest in mathematics (after accounting for interest in English classes)?

(Report answer accurate to 3 decimal places.)

( 3b ) What is the p-value for this slope?   
(Report answer accurate to 4 decimal places.)

( 3c ) For the year-10 group, is the influence of interest in general academics on interest in mathematics statistically significantly different from zero?

• yes
• no

( 4a ) When examining the second group (year-10), what is the estimated value for the influence of interest in English classes on interest in mathematics (after accounting for interest in general academics)?

(Report answer accurate to 3 decimal places.)

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

( 4c ) For the year-10 group, is the influence of interest in English classes on interest in mathematics statistically significantly different from zero?

• yes
• no

Answer 1

To answer the question related to Year-8 Students we need to fit a multiple regression model taking Interest in Mathematics as dependent variable and Interest in General Academics and English Classes as independent variable. The regression output is as below:

	Coefficients	Standard Error	t Stat	P-value
Intercept	7.613	11.643	0.654	0.5219
General Academics	0.256	0.198	1.289	0.2145
English Classes	0.342	0.128	2.678	0.0159
R Square	0.3670	Adjusted R Square	0.2925

Answer(1a): The estimated value for the influence of interest in general academics on interest in mathematics after accounting for interest in English classes is given by the regression coefficient of General academics which is given in above regression output.

Hence the estimated value for the influence of interest in general academics on interest in mathematics = 0.256

Answer(1b): The p-value for this slope is 0.2145

Answer(1c):

We have to test

H0: b general academics = 0

H1: b general academics ≠ 0

for this problem we have α=0.02 and the obtained p-value for this slope is greater than 0.02 which suggest that we do not have enough evidence against H0 to reject it so we fail to reject H0 and we cannot conclude that the influence of interest in general academics on interest in mathematics statistically significantly different from zero.

The answer is No

Answer(2a): The estimated value for the influence of interest in English classes on interest in mathematics after accounting for interest in general academics is given by the regression coefficient of English classes which is given in above regression output.

Hence the estimated value for the influence of interest in English classes on interest in mathematics = 0.342

Answer(2b): The p-value for this slope is 0.0159

Answer(2c):

We have to test

H0: b English classes = 0

H1: b English classes ≠ 0

for this problem we have α=0.02 and the obtained p-value for this slope is less than 0.02 which suggest that we have enough evidence against H0 to reject it so we reject H0 and we can conclude that the influence of interest in English classes on interest in mathematics statistically significantly different from zero.

The answer is Yes

To answer the question related to Year-10 Students we need to fit a multiple regression model taking Interest in Mathematics as dependent variable and Interest in General Academics and English Classes as independent variable. The regression output is as below:

	Coefficients	Standard Error	t Stat	P-value
Intercept	78.385	12.373	6.335	7.47E-06
General Academics	-0.036	0.159	-0.227	0.8228
English Classes	-0.575	0.145	-3.976	0.0010
R Square	0.48185	Adjusted R Square	0.420891

Answer(3a): The estimated value for the influence of interest in general academics on interest in mathematics after accounting for interest in English classes is given by the regression coefficient of General academics which is given in above regression output.

Hence the estimated value for the influence of interest in general academics on interest in mathematics = -0.036

Answer(3b): The p-value for this slope is 0.8228

Answer(3c):

We have to test

H0: b general academics = 0

H1: b general academics ≠ 0

for this problem we have α=0.02 and the obtained p-value for this slope is greater than 0.02 which suggest that we do not have enough evidence against H0 to reject it so we fail to reject H0 and we cannot conclude that the influence of interest in general academics on interest in mathematics statistically significantly different from zero.

The answer is No

Answer(4a): The estimated value for the influence of interest in English classes on interest in mathematics after accounting for interest in general academics is given by the regression coefficient of English classes which is given in above regression output.

Hence the estimated value for the influence of interest in English classes on interest in mathematics = -0.575

Answer(4b): The p-value for this slope is 0.0010

Answer(4c):

We have to test

H0: b English classes = 0

H1: b English classes ≠ 0

for this problem we have α=0.02 and the obtained p-value for this slope is less than 0.02 which suggest that we have enough evidence against H0 to reject it so we reject H0 and we can conclude that the influence of interest in English classes on interest in mathematics statistically significantly different from zero.

The answer is Yes