Lecture 31- Fitting Simple linear Regression Models

Question 1

Write down the equation for a fitted model? What does a fitted model allow us to do? How does this model change when we are wanting to predict y?

Answer 1

• Equation at the bottom of slide 579
• The fitted model allows us to calculate an estimate of the mean response (mean of Y) given any value of x.
• Equation at bottom of slide 580, the best we can do to predict y is to predict the mean value

Question 2

What does the data for a similar linear regression consist of?

Answer 2

Pairs of values

Question 3

What notation in stats denotes a random variable?

Answer 3

Upper case roman letter

Question 4

What is the estimated error or residual term in a linear regression model given by?

Answer 4

The difference between the observed value Yi and the the value of Y predicted by the fitted line estimate (triangle yi)- it’s the variation from the average/ line of best fit.

Question 5

A line that best describes the relationship between the two random variables X and Y will… How do we do this?

Answer 5

• Minimize the residual terms over all observations
• We can’t just take the absolute values of residuals and sum them to give an accurate representation of whether the line is good or not because the points above the line (positive values) and below the line (negative values) will cancel each other out.
• Instead we take the square of the residuals: the line of best fit minimizes the sum of the squares of residuals (method of least squares)

Question 6

Estimate B1 (slope) and B0 (intercept) based on example data on slide 593…

Answer 6

Answers on slide 594 and 595

Question 7

For interpretation of intercept what is needed for it to be sensible?

Answer 7

-If close to range of data: regression line may not hold at this point if far from data

Question 8

What function in R is used to fit a linear regression model?

Answer 8

model1= lm(y-x)