Question

A study was conducted with vegetarians to determine if the number of grams of protein they

ate daily was related to their diastolic blood pressure. The data are as follows:

Grams of Protein (x):

4

6.5

5

5.5

8

10

9

8.2 10.5

Diastolic BP (y):

62

79

83

82

84

92

88

86

95

Determine if there is a significant relationship between the variables, and if there is, give the

equation of the regression line and predict the diastolic blood pressure of a vegetarian who

consumes 11 grams of protein per day. Use

α

= 0.05.

Answer 1

Solution:

The null and alternative hypotheses are:

The correlation between the two variables is:

Under the null hypothesis, the test statistic is:

Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and conclude that there is a significant relationship between the variables

We can use the excel regression data analysis tool to find the least-squares regression equation. The excel output is given below;

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.859
R Square	0.738
Adjusted R Square	0.701
Standard Error	5.173
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	528.909	528.909	19.766	0.003
Residual	7	187.313	26.759
Total	8	716.222
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	57.0406	6.1842	9.2235	0.0000	42.4172	71.6640
Grams of Protein (x):	3.5627	0.8014	4.4459	0.0030	1.6678	5.4577

Therefore, the regression equation is:

Therefore, the predicted value for 11 grams is: