Question

Detailed interviews were conducted with over 1,000 street vendors in the city of Puebla, Mexico, in order to study the factors influencing vendors’ incomes. Vendors were defined as individuals working in the street and included vendors with carts and stands on wheels and excluded beggars, drug dealers, and prostitutes. The researchers collected data on gender, age, hours worked per day, annual earnings, and education level. These data are saved in STREETVEN file. Consider an interaction model ? = ?0 + ?1?1 + ?2?2 + ?3?1?2 + ? for the vendor’s mean annual earning ?(?). ?ℎ??? ? = ?????? ????????,?1 = ??? ??? ?2 = ℎ???? ?????? ??? ???.

a. Use statistical software R to fit the interaction model and provide the summary of the model. Also write least squares prediction equation. b. What is the estimated slope relating annual earnings (y) to age (x1) when number of hours worked (x2) is 10? Interpret the result. c. What is the estimated slope relating annual earnings (y) to hours worked (x2) when age (x1) is 40? Interpret the result. d. Conduct a hypothesis test to decide whether age (x1) and hours worked (x2) interact. Write your conclusion.

PLEASE PROVIDE THE CODE FOR R STUDIO or screenshot

VenNum   Earnings   Age   Hours
21   2841   29   12
53   1876   21   8
60   2934   62   10
184   1552   18   10
263   3065   40   11
281   3670   50   11
354   2005   65   5
401   3215   44   8
515   1930   17   8
633   2010   70   6
677   3111   20   9
710   2882   29   9
800   1683   15   5
914   1817   14   7
997   4066   33   12

Answer 1

(a) using R the least Square interaction model is found to be:

y= 1041.894-13.238*x1 + 103.306*x2 +3.621*x1*x2

(b) the estimated slope of y to x1 when x2 is constant = 13.238 . This means that for an unit increase in age, the earnings decreases by 13.238 ( since the sign is negative, earnings decrease)

(c) The estimated slope of y to x2 when x1 is constant = 103.306 . This means that for an unit increase in hours , the earnings increases by 103.306 ( since sign is positive, earnings increase)

(d) from the R output, we see that pvalue corresponding to interaction is 0.366 > .05 . Hence x1 and x2 don't interact.

R codes and output :
y=c(2841,1876,2934,1552,3065,3670,2005,3215,1930,2010,3111,2882,1683,1817,4066)
x1=c(29,21,62,18,40,50,65,44,17,70,20,29,15,14,33)
x2=c(12,8,10,10,11,11,5,8,8,6,9,9,5,7,12)
f=lm(y~x1+x2+(x1*x2))
summary(f)