这是一个美国的数学Online代考，主要与R线性回归模型相关

Problem 1 Exercise 4.8 (b) from the TEXT.

Problem 2 Given data in Table 6.2 (attached), the response variable is nt, representing

the number of surviving bacteria (in hundreds) after being exposed to X-ray for t intervals.

The predictor variable is t.

1) First regress nt on time t, plot residuals against the fitted values n^t. Conclude if

the relationship between the mean response and the predictor is linear.

2) Use data transformation on the response variable, i.e., regress log(nt) on t.

• What is the regression line equation?

• Plot residuals against the fitted values, and conclude if the violation of the ”L”

assumption still exists.

Problem 3 Given data in Table 6.6 (attached), the response variable Y is the number

of injury incidents, and the predictor variable N is the proportion of flights.

1) First regress Y on N, plot residuals against the fitted values Y^ . Conclude if error

is heteroscedastic, i.e., the ”E” assumption is violated.

2) Use data transformation on the response variable, i.e., regress pY on N. The

rationale behind this transformation is that the occurrence of accidents, Y , tends to

follow the Poisson probability distribution, and the variance of pY is approximately

equal to 0.25, see Table 6.5.

• What is the regression line equation?

• Plot residuals against the fitted values, and conclude if there is still evidence

of heteroscedasticity.

Problem 4 Given the data in Table 6.9 (attached), the response variable Y is the

number of supervisors, and the predictor variable X is the number of supervised workers.

Based on empirical observation, it is hypothesized that the standard deviation of the error

term i is proportional to xi:

• Use the weighted least squares (WLS) method to fit the model. Provide the regression

equation.

• Use data transformation method to transform Y to Y 0 = Y=X, and transform X to

X0 = 1=X (see equations 6.11 and 6.12), and then use the ordinary least squares

(OLS) method to regress Y 0 on X0. Provide the regression equation.

• Compare the results from the above two methods and conclude if the two methods

are equivalent. You can compare the residual vs fitted value plot side by side and

conclude if they have the same effect in terms of removing heteroscedasticity.

Problem 5 For the data in Problem 4, use OLS without data transformation to fit

the model, i.e., directly regress Y on X, and compare the variances of the coefficients

Var(β^0) and Var(β^1) with their counterparts obtained by using WLS, conclude which

method yields smaller variances.