For each individual in a sample, you have recorded the heartbeat rate ( at rest)

Question

For each individual in a sample, you have recorded the heartbeat rate ( at rest) and the average number of hours per day the person spends socializing. You intend to explore the connection. a.) In what case will you make the heartbeat the explanatory variable, and in what case will you make it the response variable? b.) How will this decision affect your results (the correlation and the regression line)? c.) How will the correlation change if you measure the socializing time in minutes instead of hours?

Explanation / Answer

a) When we will try to predict a person's socialising time by seeing his heartbeat rate[his socialising time is unknown to use],we then use heartbeat rate as a predictor . When we know a person;s socialising time and dont know the heartbeat rate and want to predict it,then for bilding a model we need to use heartbeat rate as a predictor.

b) As we know ,regression coefficient of y on x is b1=r*s_y/s_x for linear regression where r is the correlation,s_y is the standard deviation for the response variable,s_x is the standard deviation for the predictor variable.So,we can clearly see that the setup we use for using hertbeat rate as response is totallly different from the setup we use for using heartbeat rate as a predictor,hence the correlation will not change in two cases but the regression coefficient will chance and hence the regression line(or curve) will also change.

c)So,suppose S be the socialising time measured in hours,now if we measure them in minutes,then the new variable S1 meaured in minutes,will be related to S by the equation S1=S*60 . So,this is just a scale transformation.So,using invariance property of absolute vale of correlation under scale transformation,we can say that the correlation will not change if the socialising time is measured in minutes.

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