Question

The scatter diagram for the data set below is shown. (a) given that x=4.5, sx =3.2710854,y=sy =2,4094951, and r=-09680697 determibe the least-squares regression line (b) Graph the least-squares regression line on scatter diagram x 0 2 4 5 7 9 y 7.8 5.2 4.7 4.7 2.9 1.6 (a) y= blankx + blank (round to four decimals as needed)

Answer 1

Using R, we have

CODE:

x <- c(0,2,4,5,7,9)
y <- c(7.8,5.2,4.7,4.7,2.9,1.6)
a <- lm(y~x)
mean(x)
mean(y)
sd(x)
sd(y)
cor(x,y)
a
plot(x,y)
lines(x,fitted(a))

OUTPUT:

> x <- c(0,2,4,5,7,9)
> y <- c(7.8,5.2,4.7,4.7,2.9,1.6)
> a <- lm(y~x)
> mean(x)
[1] 4.5
> mean(y)
[1] 4.483333
> sd(x)
[1] 3.271085
> sd(y)
[1] 2.117939
> cor(x,y)
[1] -0.9714259
> a

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x  
7.314 -0.629  

> plot(x,y)
> lines(x,fitted(a))

So, the regresssion lie is ,

Y = 7.314 - 0.629 - X

Note: The standard deviation and correlation coefficient you have provided is slightly wrong. Please check it through my answer.