I don’t have csv for this problem but can you help on the process for each

Question

Problem I. Continuing on from HW1 Problem 1

We are still interested is studying the relationship between egg shell thickness and log concentration of

DDE. Use the regression results from the DDEeggshell.csv dataset to answer the following questions.

a. Using the formulas presented in class and R, compute βˆ

1. Hint: Your result should agree with HW1

results.

b. Using the formulas presented in class and R, compute βˆ

0. Hint: Again, your result should agree with

HW1 results.

c. Assume you also fit the following line to the data, Yˆ

i = 2.45 -0.5xi. Show that the RSS for this second

line is NOT as good as the RSS from your least squares line above. You may use R to perform your

computations.

d. Evaluate the four assumptions of your linear model (from HW1) with graphics when possible. Does the

data conform to the assumptions or not. Assess and discuss each assumption separately.

e. Using the formulas presented in class and R, compute the leverage for the observations in the dataset.

Show your work. Assess whether any of these values are large or not.

f. Using the formulas presented in class and R, compute the standardized residuals for the observations in

the dataset. Show your work. Assess whether any of these values are large or not.

g. Using the formulas presented in class and R, compute the influence of each observation in the dataset.

Show your work. Assess whether any of these values are large or not.

h. Now that you computed each observation’s leverage, standardized residual and influence, does any of

the observation(s) need to be followed-up further with the person who collected the data?

Answer 1

I would have to see the specific data, but here are some hints.

a/b. Assuming standard OLS/Linear Regression the formula for calculating the slope coefficient is cov(x,y)/var(x). In your case, cov(log concentration dde, shell thickness)/var(log concentration dde). In R, one way to calculate this is with the lm() command. I recommend something like this:

model <- lm(shell thickness ~ log concentration dde, data = csv)

summary(model)

c. residuals are the vertical distance between your model's prediction and the true value. In R, consider the following steps:

1. y_hat <- 2.45 - 0.5*(log concentration dde)
2. resid <- shell thickness - y_hat
3. rss_new <- sum(resid^2)
4. You should have the RSS from the previously fitted model
5. Show that the RSS from the previously fitted model is smaller than the RSS from this new model

d. The main Gauss-Markov assumptions (linear model assumptions) are:

1. homoskedasticity (constant variance of error terms)
2. independent variable (x's) are unrelated to error term
3. errors have a mean of zero
4. no multicollinearity if you have multiple x's (i.e the covariance between x's is essentially 0)

You can check that these assumptions are satisfied by graphing the residuals. Consider either a histogram of the residuals or a scatter plot of the residuals with log concentration of DDE on the x-axis.

I hope this helps.