USE RSTUDIO TO ANSWER THE FOLLOWING QUESTIONS. PRESENT R CODES AND SCREENSHOTS OF EVERY OUTPUT WITH THE CODE AND ASSIGN THE QUESTION NUMBER TO THE ANSWER.

In the preliminary studies of a new drug, a pharmaceutical firm needs to obtain information on the relationship between the dose level and potency of the drug. In order to obtain this information, a total of 18 test tubes are inoculated with a virus culture and incubated for an appropriate period of time. Three test tubes are randomly assigned to each of 5 different dose levels. The 18 test tubes are then injected with the randomly assigned dose level of the drug, the measured response is the protective strength of the drug against the virus culture. Due to a problem with a few of the test tubes, only 2 responses were obtained for dose levels 4, 8 and 32.

The data are:

code in R: dose <- c(2,2,2,4,4,8,8,16,16,16,32,32,64,64,64)

response <- c(5,7,3,10,14,15,17,20,21,19,23,29,28,31,30)

1. We will first fit a regression model to the raw data. Plot the data in a scatterplot and run a bivariate regression. Comment on the relationship between the covariate and response.

2. Examine the plot of the residuals vs fitted values. Does there appear to be a problem? Use two to three words to answer this question. 3. Often in drug evaluations, a logarithmic transformation of the dose level will yield a linear relationship between the response variable and the independent variable. Let x=log(dose). Plot the response of the drug vs the natural log of the dose levels (attach graph in PDF file). Does it appear that a linear model is appropriate? Answer Yes/No

4. Fit the linear regression model to these data, report the following (4 decimals and no scientific notation):

bo =

b1 =

Multiple R-squared

p-value of the b1 coefficient

5. Prepare the plot of the residuals vs the fitted values (and attach it to the PDF). Examine the QQplot of the residuals vs the theoretical normal quantiles. Answer these questions: does the linear model seem appropriate? Does the normality assumption appear to be violated? Comment on these results.

6.What is change in the response variable for a 5% change in log(dose)?

7. Calculate and report a 95% confidence interval for the slope parameter LB, UB using 4 digits after the decimal.

8. Do you reject the null hypothesis Ho: B1=0? Yes/No [a]