Question

Researchers want to examine whether or not weight can predict systolic blood pressure. They collect weight in pounds and blood pressure measurements for 31 adult men. For your convenience, I have prepared an Excel file with the data :

Weight	Systolic Blood Pressure
162	134
163	149
167	128
168	129
173	128
173	118
174	133
175	138
184	143
184	147
185	144
218	137
186	149
188	137
235	138
189	150
189	128
194	153
195	154
196	120
196	154
177	159
207	134
209	160
211	162
211	143
212	164
217	166
182	167
220	168
221	169

Test the relationship between weight and systolic blood pressure at the α = 0.05 level. While doing the calculations, leave four decimal places as appropriate. Round your final answer to two decimal places.

How do you interpret this finding? For every one unit increase in weight, there is a corresponding ___________ ______________ in systolic blood pressure.

Based on this information, the researcher should make the decision to ___________.

What percentage of variance in systolic blood pressure is explained for by weight?

What is the value for the correlation between weight and systolic blood pressure?

What is the best predicted value for systolic blood pressure given that a man weighs 175 pounds?

Answer 1

Here the dependent variable y = Systolic Blood Pressure

independent variable x = weight

To find the relationship between X and Y Goto Data in menu bar ---> Data Analysis ---> Regression

Now enter the weights column in X

and Systolic BP column data in Y.

select labels option and then click on Ok.

The results are displayed in new wor book.

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.456
R Square	0.208
Adjusted R Square	0.181
Standard Error	13.308
Observations	31

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1347.582	1347.582	7.608485	0.009953
Residual	29	5136.354	177.1156
Total	30	6483.935

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	78.8608	24.1898	3.2601	0.0028	29.3872	128.3344
Weight	0.3453	0.1252	2.7583	0.0100	0.0893	0.6013

Slope coefficient b = 0.3453

For every one unit increase in weight, there is a corresponding 0.3453 unit increase in systolic blood pressure.

Based on this information, the researcher should make the decision to Reject H0 and conclude that there is a significant linear relation between X and Y.

What percentage of variance in systolic blood pressure is explained for by weight? = R2 = 0.208

20.8% of variance in systolic blood pressure is explained for by weight.

What is the value for the correlation between weight and systolic blood pressure?

Sqrt(R2) = 0.456

What is the best predicted value for systolic blood pressure given that a man weighs 175 pounds?

Y = 78.8608 + 0.3453 *X

for X = 175

Y = 78.8608 + 0.3453 *175 = 139.2883.