Question

Listed below are systolic blood pressure measurements​ (in mm​ Hg) obtained from the same woman. Find the regression​ equation, letting the right arm blood pressure be the predictor​ (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05.

mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in Listed below are systolic blood pressure measurements the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05. i Data Table Right Arm 100 99 91 75 74 m Left Arm 174 16F 180 147 146 Click the icon to view the critical values of the Pearson correlation coefficient r Critical Values of the Pearson Correlation Coefficient r 0.05 NOTE p = 0 against H, : p#0. otest Ho: 0.01 The regression equation is y x o 979 (Round to one decimal place needed.) reject Ho if the absoluter 0.811 0.754 0.917 Given he right arm is 85 mm Hg, the best predicted systolic blood pressure in the left arm is mm Hg. 0.875 han the eritical value in the table. (Round to one decimal olace as needed.) U.r 0.632 0.602 0.765 0.735 10 1 12 0.576 0.708 14 0.532 0.514 n 665 15 0.641 16 0.497 0.623 0 590 18 0.456 0.444 1C 0.575 20 0.561 483 0.361 35 0.335 0.430 40 0.312 0.402 0.378 60 0.254 0 330 0.236 0.305 0.286 70 80 0.220 0 196 100

Answer 1

Solution:

Here, we have to find the regression model for the prediction of the dependent variable or response variable systolic blood pressure in the left arm based on the independent variable or explanatory variable systolic blood pressure in the right arm.

The required regression model is given as below:

Regression Statistics
Multiple R	0.864491266
R Square	0.74734515
Adjusted R Square	0.663126866
Standard Error	9.084817982
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	732.3982467	732.3982467	8.873906226	0.058648137
Residual	3	247.6017533	82.53391776
Total	4	980
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	68.98747652	31.81981253	2.168066718	0.118671555	-32.27736829	170.2523213
Right arm	1.070757671	0.359446101	2.978910241	0.058648137	-0.073160244	2.214675586

From above regression model, the p-value is given as 0.058648137 which is greater than α = 0.05, so we do not reject the null hypothesis. There is insufficient evidence to conclude that there is statistically significant relationship between the given two variables systolic blood pressure in the left arm and systolic blood pressure in the right arm.

The required regression equation is given as below:

ŷ = 69.0 + 1.1*x

Where, ŷ = Predicted systolic blood pressure in the left arm and x = systolic blood pressure in the right arm.

Now, we have to find the predicted systolic blood pressure in the left arm for the given systolic blood pressure of 85 mm Hg in the right arm.

So, we are given x = 85

ŷ = 69.0 + 1.1*x

ŷ = 69.0 + 1.1*85

ŷ = 162.5

Given that the systolic blood pressure in the right arm is 85 mm Hg, the best predicted systolic blood pressure in the left arm is 162.5 mm Hg.