Answer :
Answer:
c) [tex]y=16.57+1.83x[/tex]
Step-by-step explanation:
Equation for regression line of y on x is given as
[tex]\hat{y}=mx+b --- (1)[/tex]
where
[tex]\hat{y}[/tex] = predicted value
m = slope of line
b = intercept
m and b are found as
[tex]m=r\frac{S_{y}}{S_{x}}---(2)\\\\b=\bar{y}-m\bar{x}---(3)[/tex]
r = correlation coefficient = 0.88
Sx = standard deviation for independent variable x = 13
Sy = standard deviation for dependent variable y = 27
[tex]\bar{x}[/tex] = mean value of independent variable x = 21
[tex]\bar{x}[/tex] = mean value of dependent variable y = 55
Substituting these values in (2) and (3)
[tex]m=r\frac{S_{y}}{S_{x}}\\\\m=(0.88)\frac{27}{13}\\\\m=1.83[/tex]
[tex]b=\bar{y}-m\bar{x}\\\\b=55-(1.827)(21)\\\\b=16.57[/tex]
Putting these values of m and b in (1)
[tex]y=1.83x+16.57[/tex]