The Ozone data was created in a study of the relationship between atmospheric ozone concentration and meteorology in the Los Angeles Basin in 1976.

The Ozone data was created in a study of the relationship between atmospheric ozone concentration and meteorology in the Los Angeles Basin in 1976. A number of cases with missing variables have been removed for simplicity.

The data frame has 330 observations on the following 10 variables:

O3: Ozone conc., ppm, at Sandbug AFB

vh: a numeric vector

wind: wind speed

humidity: a numeric vector

temp: temperature

ibh: inversion base height

dpg: Daggett pressure gradient

ibt: a numeric vector

vis: visibility

doy: day of the year

You can access the data frame using the following statement: data(ozone, package = “faraway”)

Question 1

Fit a model with O3 as the outcome and temp and humidity as predictors. Which coefficients are significant at the 5% level?

Question 2

Fit the same model but add an interaction between temp and humidity.

Has the adjusted R2 increased compared to the previous model?

Is the interaction coefficient significant?

Is the temp variable significant?

Should we remove the temp variable while keeping the interaction?

Hint: use * to define an interaction term. See and refer to Lesson 8, Slide 50.

Question 3

Create a standardized residuals vs fitted plot. Do you detect any issues?

Hint: See Lesson 6. Slide 11.

Question 4

Create a Q-Q plot and histogram of the standardized residuals. Do you see any issues?

Hint: See Lesson 6, Slide 26.

Question 5

Use the Box-Cox method to find the optimal exponent for a power transformation of the outcome. What is the exponent that you found?

Hint: See Lesson 8, Slide 14.

Question 6

Create a new variable for the transformed outcome based on the maximum likelihood exponent and fit a new model with the same predictors (including the interaction term). Show the regression output.

Hint: See Lesson 8, Slide 21.

Question 7

Create a standardized residuals vs fitted plot for the new model. Do you see any difference compared to the previous plot?

Question 8

Create a Q-Q plot and histogram of the standardized residuals for the new model. Do you see any difference compared to the previous plot and histogram?

Please help me solve these question based on the file I provided. Thank you!