Question

1. Use the built in R dataset called “mtcars.” You can see what variables this dataset contains by typing help(mtcars). Calculate a scatter plot for the variables: wt and mpg. Also, calculate the correlation coefficient. Calculate a least squares line and plot it in the scatterplot.

Answer 1

I have attached the code below as well as the output.

data=mtcars help(data) x=data$wt y=data$mpg plot(x,y) cor(x,y) model=lm(y~x) yest=37.285-5.344*x plot(x,y) lines(x,yest,type="l")

The scatter plot is as follows:

where my x variate corresponds to weight and y variate corresponds of mpg.

To find correlation between them cor command is used and output is:

cor(x,y)
[1] -0.8676594

hence the correlation is -0.8676594.

The least square estimates are as follows

Coefficients:
(Intercept) x
37.285 -5.344

Hence the model is

Yest=37.285-5.344*X

Therefore the least squares line is calculated and the graph is as follows

Hence the line is the least square line and the points are scatterplot.