Question

For a sample of five married couples, the variables x = age of younger partner and y = age of older partner were recorded.

?x	20	25	26	30	35
?y	21	30	35	31	37

NOTE: SXX = 126.8, SXY = 116.2, SYY = 152.8, ?¯x¯ = 27.2, and ?¯y¯ = 30.8.

Compute the slope of the least squares line correct to three decimal places of accuracy.

Slope = ?=b=

Answer 1

Solution:

Suppose the regression equation is:

y= a+bx where a= intercept and b=slope

Given: SXX = 126.8, SXY = 116.2, SYY = 152.8, xbar= 27.2, and ybar= 30.8.

The slope of the regression line is given by;

b= Sxy/Sxx = 116.2/126.8 = 0.916

Also, using R software:

x<- c(20,25,26,30,35) ;

y<- c(21,30,35,31,37);

fit=lm(y~x);fit;

Output:

Call:

lm(formula = y ~ x)

Coefficients:

(Intercept) x  

5.8738 0.9164  

Intercept a= 5.874 and slope b=0.916