Question

Data was gathered on 29 people to investigate the relationship between age (x) and Systolic Blood Pressure (y). The scatter plot and Summary Statistics are shown below.

Use the scatterplot and Summary Statistics to describe the direction and strength of the relationship between Age and Systolic Blood Pressure, referencing the appropriate statistic.

The graph is positive linear as it is going upwards where it also provides a correlation of 0.844 this shows a strong relationship between age and systolic pressure

  

b)   What is the regression equation for predicting Systolic Blood Pressure from Age?

  

What are the Null and Alternate hypotheses for testing whether there is a significant relationship between Age and Systolic Blood Pressure?

      i) How much of the variation in Systolic Blood Pressure is explained by this regression model?

                     

ii)) Is it reasonable to use this regression equation to predict Systolic Blood Pressure from the Age?

Answer 1

data is not given , so it is not possible to find the regression equation. but other question can be answered as

This is simple linear regression equation y=a+bx , analysis and

b=r*sd(y)/sd(x) and a=mean(y)-b*mean(x)

where y=systolic blood pressure and x=age

here the null hypothesis H0:b=0 and alternate hypothesis Ha:b0

since r=0.844 and it is significant ( mentioned inf first part of question), so there is significant relationship between age and systolic blood pressure

(i) for the simple linear regression case the explained variation=r*r=0.844*0.844=0.7123

i.e. 71.23% of variation is explained by the regression model

(ii) since the correlation coefficient is significant so , it is reasonable to use this regression equation to predict systolic blood pressure from the age.