Question

Starting salaries for accountants in Tampa follow those of many U.S. cities. The table bellow shows starting salaries (in thousands of dollars) and the cost of living index for 5 metropolitan areas.    A regression analysis will help provide explanation on how cost of living explains salary in this sample.

Salary in Thousands $

  

1. (2pt) Explain the relationship of cost of living and salary

According to what is shown in the scatter diagram.

Cost of Living Index

2. (8pt)Use the least squares method (OLS) to develop an estimated regression equation for this problem (That is, calculate bo and b1)

Metropolitan area	Index	Salary (thousand $)
Oklahoma City	46	19
Tampa	35	10
Atlanta	50	27
Sacramento	65	29
Honolulu	59	25
Mean	51.0	22.0

3. (2pt) Write down the estimated regression equation.    

4. (3pt) Provide an interpretation for the slope.

(5pt) Provide an interpretation for the intercept of the estimated regression equation

Answer 1

I used R software to solve this problem,

R code:

salary=c(19,10,27,29,25)
index=c(46,35,50,65,59)

a)
plot(index,salary) # it gives scatter plot

From scatter plot we see that there is highly positive correlation between cost of living index and salary.

b)

fit=lm(salary~index) # it gives least square regression equation

fit

Call:
lm(formula = salary ~ index)

Coefficients:
(Intercept) index
-8.4871 0.5978

b0= -8.4871

b1 = 0.5978

c)

Required least square equation is,

salary = -8.4871 + 0.5978 index

d)

Interpretation of slope: When cost of living index increased by 1 unit then salary increased by 0.5978 * 1000 = 597.8 dollars.

Interpretation of intercept: When cost of living index is zero then salary is -8.4871 * 1000 = -8487.1 dollars.