A researcher found that age (X) and annual income (Y) were correlated with r = 0.50....

A researcher found that age (X) and annual income (Y) were correlated with r = 0.50. For age, M = 50 and SD = 10. For annual income (in thousands of dollars), M = 60 and SD = 10. The intercept of the regression line was found to be 35. What is the value of the slope of the regression line?

Expert Solution

## Q ) A researcher found that age (X) and annual income (Y) were correlated with r = 0.50. For age, M = 50 and SD = 10. For annual income (in thousands of dollars), M = 60 and SD = 10. The intercept of the regression line was found to be 35. What is the value of the slope of the regression line?

Answer : Here independent variable : age = x

and dependent variable : annual income = y

r : correlation coefficient between x and y = 0.50

for age : mean and standard deviaton are : xbar = M = 50 and Standard deviation = SD (x) = 10

and for annual income : mean and standard deviation are : ybar = M = 60 and standard deviation = SD(y) = 10

here y intercept value = 35

we have to find out slope value :

formula for slope : = r * (SD(y) / SD(x) )

= 0.50 * ( 10 /10 )

= 0.50

slope is 0.50

## note : Where r is the correlation between x and y and SD(x) and SD(y) are the standard deviations of the x values and the y values , respectively , we can simply divide SD(y) by SD(x) and multiply the resuly by r we can get slope value

orchestra answered 1 year ago

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