This is written using rStudio only. Please only help if you are using that program with explanations please. Thank you

Here are all instructions with questions. The data frame being used will be provided at the bottom of this question.

## Load all packages used in this assignment in the code following chunk.

```{r, message=FALSE}

```

# Anesthesia

A study was conducted whereby the type of anesthetic (A or B), nausea after the surgery (Yes or No), the amount of pain medication taken during the recovery period, and age for a random sample of 72 patients undergoing reconstructive knee surgery.

The data is in the file "anesthesia" AT THE BOTTOM OF THE PAGE

Load the data and obtain the output from R for the logistic regression model with nausea as the response variable and the type of anesthetic as the explanatory variable. Summarize it using summary() function.

Use this model to address questions 1-5 below.

Note: "Yes" should correspond to Y=1 for the response and anesthetic A should be the reference category in the model.

## Question 1 (1 point)

Is the coefficient of anesthetic (labeled as anestheticB in the output) statistically significantly different from 0 at a 5% level of significance? (Yes or No)

## Question 2 (2 points)

Report the p-value for the hypothesis test on that coefficient. Round it to 4 decimal places.

Convert the estimated coefficient of anestheticB to an odds ratio. select the correct interpretation of it.

## Question 3 (2 points)

Select the correct interpretation of the odds ratio computed directly from the coefficient of anestheticB.

a. The odds of having nausea with anesthetic B are 4.6 times the odds of having nausea when using anesthetic A.

b. The odds of having nausea with anesthetic A are 0.217 times the odds of having nausea when using anesthetic B.

c. The odds of having nausea with anesthetic A are 21.7% more than for anesthetic B.

d. The odds of having nausea with anesthetic B are 78.3% less than for anesthetic A.

e. The odds of having nausea with anesthetic B are -1.526 times the odds of having nausea when using anesthetic A.

## Question 4 (1 point)

Report the AIC for the logistic regression model with nausea as the response variable and the type of anesthetic as the explanatory variable. Round it to 1 decimal place.

## Question 5 (1 point)

Compute the McFadden pseudo-$R^2$ for the logistic regression model with nausea as the response variable and the type of anesthetic as the explanatory variable. Round it to 3 decimal places.

Fit the logistic regression model with nausea as the response variable and only the amount of pain medication (painmed) as the explanatory variable. Summarize it using summary() function. Use this model to address questions 6-10 below.

## Question 6 (2 points)

Is the coefficient of painmed statistically significantly different from 0 at a 5% level of significance?

(Yes or No)

## Question 7 (2 points)

Report the p-value for the hypothesis test on that coefficient. Round it to 4 decimal places.

Convert the estimated coefficient of painmed to an odds ratio. select the correct interpretation of it.

## Question 8 (2 points)

Select the correct interpret ion of the odds ratio computed directly from the coefficient of painmed.

a. The odds of having nausea increase by a factor of 1.038 for each unit increase in painmed.

b. The odds of having nausea increase by a factor of 0.037 for each unit increase in painmed.

c. The odds of having nausea decrease by a factor of 1.038 for each unit increase in painmed.

d. The odds of having nausea increase by 0.037 for each unit increase in painmed.

e. The odds of having nausea decrease by 1.038 for each unit increase in painmed.

## Question 9 (1 point)

Report the AIC for the logistic regression model with nausea as the response variable and the amount of pain medication as the explanatory variable. Round it to 1 decimal place.

## Question 10 (1 point)

Compute the McFadden pseudo-$R^2$ for the logistic regression model with nausea as the response variable and the amount of pain medication as the explanatory variable. Round it to 3 decimal places.

Fit the logistic regression model with nausea as the response variable and painmed, anesthetic and age as the explanatory variables. Summarize it using summary() function.

## Question 11 (2 points)

Select the explanatory variables for which the coefficient(s) are significantly different from 0 at a 5% level of significance.

a. painmed

b. anesthetic

c. age

Use the likelihood ratio test to compare the model with only painmed as the explanatory variable to the model containing all 3 explanatory variables. Use a 10% level of significance.

## Question 12 (2 points)

Choose the correct conclusion to the likelihood ratio test to compare the models.

a. The model with all three explanatory variables is not significantly better than the model with only painmed.

b. The model with only painmed is not significantly better than the model with all three explanatory variables.

c. The test is inconclusive.

## Question 13 (1 point)

Report the p-value for this likelihood ratio test to compare models. Round it to 3 decimal places.

Which model is "best"?

## Question 14 (2 points)

Select the model that is "best" according to the AIC.

a. The model with only painmed.

b. The model with only anesthetic.

c. The model with all three explanatory variables.

## Question 15 (2 points)

Select the model that is "best" according to the McFadden pseudo-$R^2$.

a. The model with only painmed.

b. The model with only anesthetic.

c. The model with all three explanatory variables.

Use the deviance goodness of fit test to test the fit of the model with only painmed as the explanatory variable. Use a 5% level of significance.

## Question 16 (2 points)

Choose the correct conclusion to the deviance goodness of fit test.

a. The model fits.

b. The model does not fit.

c. The test is inconclusive.

## Question 17 (2 points)

Report the p-value for this deviance goodness of fit test to compare models. Round it to 3 decimal places.

Using the model with only painmed as the explanatory variable, construct a 90% confidence interval for the odds ratio relating nausea to the amount of pain medication.

## Question 18 (2 points)

Report the upper bound for this confidence interval. Round it to 3 decimal places.

Here is the dataset (Anesthesia) Used in this Question:

age	painmed	anesthetic	nausea
49.90136986	53.49	A	No
70.23561644	21.66	A	No
64.07123288	86.5	A	No
73.31506849	37.34	A	No
59.7260274	87	A	No
80.60821918	18.33	A	No
59.41643836	103.5	A	No
74.96712329	68.5	A	No
47.53424658	121.5	A	No
72.2630137	86.66	A	No
73.63013699	25	A	No
44.55342466	147	A	No
64.41643836	26.67	A	No
71.15616438	106.5	A	Yes
62.40821918	189	A	Yes
54.28219178	84	A	Yes
51.73424658	98	A	Yes
51.37808219	40	B	No
57.48219178	23.33	B	No
62.05753425	11.66	B	No
51.9369863	32.5	B	No
84.19726027	106	B	No
66.90958904	45.01	B	No
61.86849315	190	B	No
82	45	B	No
62.38356164	16.67	B	No
67.80547945	67.5	B	No
64.63013699	36.66	B	No
49.74520548	85	B	No
47.15890411	40	B	No
68.05753425	11.67	B	No
73.91506849	37.67	B	No
70.69315068	53.34	B	No
58.45205479	20	B	No
69.37260274	22.5	B	No
62.73150685	25	B	No
56.35616438	39.99	B	No
66.46575342	54.16	B	No
52.40821918	66.66	B	No
57.55616438	23.33	B	No
72.02739726	87.5	B	Yes
64.98630137	88	B	Yes
66.12876712	163	B	Yes
55.00547945	160	B	Yes
56.64657534	166.34	B	Yes
70.8109589	80.01	B	Yes
54.35068493	45	B	Yes
68.94794521	102	B	Yes
66.7890411	56.67	B	Yes
63.23561644	118.33	B	Yes
45	150	A	Yes
70	122	A	Yes
36	148	A	Yes
49	198	A	Yes
58	160	A	Yes
52	151	A	Yes
56	148	A	Yes
55	137	A	Yes
63	120	A	Yes
48	75	A	Yes
66	98	A	Yes
61	88	A	Yes
59	128	A	Yes
50	107	A	Yes
42	96	A	Yes
70	82	A	Yes
28	65	A	Yes
39	75	A	Yes
53	84	A	Yes
49	90	A	Yes
68	105	A	Yes
62	115	A	Yes