Question

Suppose we are interested in predicting lung cancer deaths (MORT) from per capita cigarette consumption (PCCC). Sample size (n) = 25 Correlation (r) = .74 Mean of PCCC = 603.636, SD of PCCC = 378.451 Mean of MORT = 20.545, SD of MORT = 11.725 <> Residentials2= 7.374

a). What is "b"

b). What is the intercept "a"

c). What is the prediction equation?

Answer 1

Let y denote values for the lung cancer deaths (MORT)

Let x denote values for per capita cigarette consumption (PCCC)

r = 0.74 (correlation coefficient of x and y)

= 20.545 ( mean of MORT)

= 11.725 (standard deviation of MORT)

= 603.636 (mean of PCCC)

= 378.451 (standard deviation of PCCC)

a) Here "b" is the slope of the regression equation

b = 0.023 (slope)

b) "a" is the intercept

To get intercept "a" we substitute the value of = 20.545 , = 603.636 , b = 0.023 in the equation = a + b

= a + b

20.545 = a + 0.023 603.636

a = 6.661

a = 6.661 (intercept)

c) If we denote as the predicted value of y

Then the predicting equation can be created substituting a = 6.661 , b = 0.023 in the equation

The predicting equation is   = 6.661 + 0.023x