Need an R code for the below questions and required necessary explanations and equations. I have attached the data work_hrs.xlsxat last of all the questions. QUESTION 11

Refer to thework_hrs.xlsxdataset. In this problem, we want to examine the effect ofwage,education(EDUC),and number of children (NCHILD) on the hours worked per week by married women (HRSWORK). The dataset contains only married women.Estimate the linear regression model. Do not use log transformations to solve this problem.

Report the value from R output and use 4 decimals(example: 0.6578) This is Model 3.

HRSWORK_hat= B0+B1WAGE+B2EDUC+B3NCHILD+

b₀=

b₁=

b₂=

b₃=

4 points

QUESTION 12

1. Interpret the coefficient ofEDUC.

4 points

QUESTION 13

1. Calculate the predicted hours worked per week by a married woman whose wage is $22 per hour, who has 17 years of education, and who has three children. Use Model3

4 points

QUESTION 14

1. Modify Model3, and add the necessary variables to estimate the average hours difference between a black women who lives in a metropolitan area with a black woman who lives in a nonmetropolitan area. This is Model4

4 points

QUESTION 15

1. Based on Model4, estimate the average hours difference between a black women who lives in a metropolitan area with a white woman who also lives in a metropolitan area

4 points

QUESTION 16

1. Refer to thework_hrs.xlsxdataset.Define the below indicator variables;hint:data$POSTGRAD=ifelse(data$EDUC>16,1,0)

LTCOLLEGE =1 if EDUC < 16, 0 otherwise

COLLEGE =1 if EDUC = 16, 0 otherwise

POSTGRAD =1 if EDUC > 16, 0 otherwise

Using the same variables from Model3, replaceEDUCwith education dummies and answer the below questions. Consider LTCOLLEGEas the reference group. Report the value from R output and use 4 decimals(example: 0.6578) This is Model 5.

What is the difference between the average hours worked by a person with aPOSTGRADdegree and a person with a college degree ?

What is the difference between the average hours worked by a person with a college degree and thosewith less than a college degree ?

5 points

QUESTION 17

1. Problem 3 (questions 17 to 20) Use ex1217 (from Sleuth3) that contains 15 variables for 60 cities. The variables included in this file are:

Response ~ Mortality: Total age-adjusted mortality from all causes, in deaths per 100,000 population

1. mean annual precipitation (in inches);
2. percent relative humidity (annual average at 1 P.M.);
3. mean January temperature (in degrees Fahrenheit);
4. mean July temperature (in degrees Fahrenheit);
5. percentage of the population aged 65 years or over;
6. population per household;
7. median number of school years completed by persons of age 25 years or more;
8. percentage of the housing that is sound with all facilities;
9. population density (in persons per square mile of urbanized area);
10. percentage of 1960 population that is nonwhite;
11. percentage of employment in white-collar occupations;
12. percentage of households with annual income under $3,000 in 1960;
13. relative pollution potential of hydrocarbons (HC);
14. relative pollution potential of oxides of nitrogen (NOX ); and
15. relative pollution potential of sulphur dioxide (SO2).

It is desired to determine whether the pollution variables (13, 14, and 15) are associated with mortality, after the other climate and socioeconomic variables are accounted for.

Note: This data has problems with influential observations and with lack of independence due to spatial correlation; ignore these issues while solving this exercise.

Use backward elimination and select the best fitting regression model involving weather and socioeconomic variables as explanatory variables (do not include variables 13,14 and 15 yet) and report the RSS value of your selected model. This is Model6

5 points

QUESTION 18

1. With mortality as the response, use Forward selection to find the best fitting regression model involving weather and socioeconomic variables as explanatory variables (do not include variables 13,14 and 15 yet). Report the RSS of the model you selected. This is Model7

5 points

QUESTION 19

1. Run Model6 and Model7 with added pollution variables (13,14,15 in their log form). Report the highest Adjusted R-squared across these models.

5 points

QUESTION 20

1. Are the pollution variables (13,14 and 15) joinly statistically significant in this model? Run the appropriate hypothesis test and report the test-statistics.

5 points

work_hrs.xlsx Sample data

HRWORK	WAGE	NCHILD	EDUC	BLACK	METRO
52	13.45	0	0	0	1
40	14.55	2	12	0	1
40	20.17	2	16	0	1
52	19.23	2	14	1	1
50	45	1	21	0	1
36	62	1	16	1	1
40	28.5	0	16	0	1
42	15	0	12	0	1
40	14.5	0	8	0	1
40	24.05	0	12	0	1
40	17.8	1	16	0	0
40	18.98	0	16	0	0
40	23	0	14	0	1
40	12.3	1	16	0	1
40	24.05	0	13	0	1
40	19.23	0	13	0	1
40	24	0	13	0	0
50	35.38	0	21	1	1
40	20	1	16	0	1
40	21.63	2	16	0	1
40	15.38	2	16	0	1
50	30.76	0	18	0	1
40	13.27	0	12	0	1
45	31.02	2	16	0	1
40	19	4	14	0	0
36	35	2	18	0	1
40	39.42	1	16	0	0
40	72.13	3	20	1	1
40	28.85	0	16	0	1
40	13.66	2	14	0	1
20	8	1	13	0	0
40	6.93	7	12	1	1
40	17.3	0	16	0	1
40	21.63	2	18	0	1
40	38.45	0	16	0	1
37	24	1	18	0	0
40	15.61	1	12	0	1
40	16.83	0	12	0	1
60	15.38	1	18	0	1
40	15.38	0	14	0	1
50	8.08	0	18	1	1
40	18.68	2	13	0	1
50	34.04	0	18	0	1
40	14.4	0	16	0	0
40	14.4	1	12	1	1
43	33.53	2	18	0	1
40	34.63	1	18	0	0
40	13	0	16	0	1
40	15.34	2	12	0	0
40	28	1	14	0	1