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A certain department store keeps track of an age and an annual income of customers who have its credit card. From a sample of 820 of such customers the following descriptive statistics had been obtained: the average age was 41 years with the standard deviation of 16 years and the average annual income was $37,290 with the standard deviation of $2,850. The correlation between the age the annual income was found to be 0.34. Answer the following questions. (Round your answers to 2 places after the decimal point).
Calculate the value of a slope.
a) 309.23 $ per year of age
b) 60.56 $ per year of age
c) 192.43$ per year of age
d) None of the above

Respuesta :

Answer: b) $60.56 per year of age

Step-by-step explanation: If the scatterplot of two variables shows a line and the correlation between them is strong, we can calculate a regression line.

Regression line is a line graph that best fits the data. Like any other line, its formula is given by

y = mx + b

with

m being the slope

b the y-intercept

The slope of the line, correlation and standard deviations of the two variables have the following relationship:

[tex]m=r\frac{S_{y}}{S_{x}}[/tex]

where

r is correlation

[tex]S_{y}[/tex] is standard deviation for the y data

[tex]S_{x}[/tex] is standard deviation for the x data

For our problem:

r = 0.34

[tex]S_{y}=[/tex] 2850

[tex]S_{x}=[/tex] 16

Calculating

[tex]m=0.34(\frac{2850}{16})[/tex]

m = 60.56

Slope for the regression line of annual income per year of age is 60.56.

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