Consider the following bivariate dataset: (3.0, 2.4) (5.0, 1.8) (6.0, 1.8) You c

Question

Consider the following bivariate dataset: (3.0, 2.4) (5.0, 1.8) (6.0, 1.8) You can do this question by hand, with your calculator, or with R. Enter all answers below rounded to 4 significant figures, but do not round intermediate results during your calculations. Determine the least squares estimates alpha and beta of the parameter of the regression line y = alpha + beta x. Use the fitted model to predict a value for y when x = 4.0 Determine the residuals r_1, r_2, and r_3. Calculate the residual sum of squares, the total sum of squares and use them to calculate the coefficient of determination R^2

Explanation / Answer

R code

R Output:

a. From the regression output, the regression equation is y= + x = 3 - 0.21429x

b. For x=4, y= 3 - 0.21429*4 = 3 - 0.85716 = 2.14284

c. From the regression output

d. From the ANOVA

Residual sum of squares(RSS) = 0.025714

Total sum of squares(TSS)= Regression sum of squares + RSS = 0.214286+0.025714 = 0.24

The coefficient of determination is given by

R2= 1-(RSS/TSS) = 1-(0.025714/0.24) = 1-0.107142=0.892858 (The same is given in regression output)

x=c(3,5,6)
y=c(2.4,1.8,1.8)
model=lm(y~x)
summary(model)
anova(model)

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