Question

Given the data of BMI of Freshman students at the beginning of Fall and Spring semester

- compute the correlation coefficient

- find the slope of the regression line

- find the intercept of the regression line

- draw the scatterplot of the data with the regression line

- predict the value of BMISP given the predictor BMIAP is 22.28

- what is the coefficient of determination and what does it tell us?

BMIAP BMISP
18.14 22.02
17.44 19.7
22.43 24.09
25.57 26.97
20.1 21.51
17.4 18.69
22.88 24.24
20.23 21.23
29.24 30.26
21.02 21.88
16.89 17.63
23.85 24.57
20.15 20.68
20.36 20.97
26.73 27.3
22.88 23.3
19.24 19.48
24.69 24.74
20.79 20.69
20.6 20.49
21.24 21.09
18.53 18.37
22.61 22.4
28.43 28.17
23.81 23.6
26.78 26.52
19.27 18.89
19.75 19.31
21.32 20.96
22.22 21.78
20.23 19.78
22.82 22.4
23.19 22.76
20.69 20.15
22.57 22.14
20.76 20.27
22.93 22.15
24.67 23.87
19.34 18.61
22.58 21.73
19.72 18.93
26.72 25.88
29.53 28.59
22.79 21.89
19.28 18.31
20.63 19.64
24.1 23.02
21.91 20.63
23.81 22.61
23.42 22.03
21.34 20.31
21.36 20.31
20.77 19.59
22.31 21.05
25.11 23.47
24.29 22.84
20.9 19.5
19.83 18.51
22.97 21.4
19.42 17.72
23.87 22.26
23.81 21.64
24.45 22.51
25.8 23.69
17.74 15.08
25.33 22.64
40.86 36.57

BMIAP BMISP
18.14 22.02
17.44 19.7
22.43 24.09
25.57 26.97
20.1 21.51
17.4 18.69
22.88 24.24
20.23 21.23
29.24 30.26
21.02 21.88
16.89 17.63
23.85 24.57
20.15 20.68
20.36 20.97
26.73 27.3
22.88 23.3
19.24 19.48
24.69 24.74
20.79 20.69
20.6 20.49
21.24 21.09
18.53 18.37
22.61 22.4
28.43 28.17
23.81 23.6
26.78 26.52
19.27 18.89
19.75 19.31
21.32 20.96
22.22 21.78
20.23 19.78
22.82 22.4
23.19 22.76
20.69 20.15
22.57 22.14
20.76 20.27
22.93 22.15
24.67 23.87
19.34 18.61
22.58 21.73
19.72 18.93
26.72 25.88
29.53 28.59
22.79 21.89
19.28 18.31
20.63 19.64
24.1 23.02
21.91 20.63
23.81 22.61
23.42 22.03
21.34 20.31
21.36 20.31
20.77 19.59
22.31 21.05
25.11 23.47
24.29 22.84
20.9 19.5
19.83 18.51
22.97 21.4
19.42 17.72
23.87 22.26
23.81 21.64
24.45 22.51
25.8 23.69
17.74 15.08
25.33 22.64
40.86 36.57

Answer 1

Solution:

A correlation coefficient and regression model for the given data for dependent variable BMISP and independent variable BMIAP is given as below:

Correlation coefficient:

	BMIAP	BMISP
BMIAP	1
BMISP	0.937073547	1

Regression Statistics
Multiple R	0.937073547
R Square	0.878106833
Adjusted R Square	0.877183399
Standard Error	1.155243367
Observations	134
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1269.079685	1269.079685	950.9154969	3.49338E-62
Residual	132	176.1655152	1.334587236
Total	133	1445.2452
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.67793662	0.635447153	4.214255439	4.61447E-05	1.42095936	3.934913879
BMIAP	0.860696906	0.02791125	30.83691776	3.49338E-62	0.805485696	0.915908115

- compute the correlation coefficient

The correlation coefficient between the dependent variable BMISP and independent variable BMIAP is given as 0.9371 which means there is a strong positive linear relationship or association exists between the dependent variable BMISP and independent variable BMIAP.

- find the slope of the regression line

The slope of the regression line is given as 0.8607 approximately.

- find the intercept of the regression line

The intercept of the regression line is given as 2.6779 approximately.

- draw the scatterplot of the data with the regression line

Required scatterplot of the data with the regression line is given as below:

- predict the value of BMISP given the predictor BMIAP is 22.28

The regression equation is given as below:

BMISP = 2.6779 + 0.8607*BMIAP

We are given BMIAP = 22.28

BMISP = 2.6779 + 0.8607*22.28

BMISP = 21.854296

BMISP = 21.8543

- what is the coefficient of determination and what does it tell us?

The coefficient of determination or the value of R square is given as 0.8781 which means about 87.81% of the variation in the dependent variable BMISP is explained by the independent variable BMIAP.