Question

Homework 4 Question 2 A large school district is reevaluating its teachers' salaries. They have decided to use regression analysis to predict mean teacher salaries at each elementary school. The researcher uses years of experience to predict salary. The resulting equation was: where Y = salary and X = years of experience. The raw data is given in the table below.

Salary Years of experience

$54,000.00 13

$42,140.00 9

$36,195.00 7

$45,000.00 9

$58,950.00 14

$56,890.00 13

$53,250.00 14

$49,800.00 11

$35,820.00 8

$74,390.00 22

$28,900.00 5

$38,690.00 8

$78,070.00 23

$64,205.00 18

$20,000.00 2

$49,000.00 12

$26,500.00 7

$32,000.00 8

a) Use Excel to develop the scatter diagram of the relationship between years of experience and salary (copy and paste your output). What can you conclude from the scatter diagram?

b) Use Excel to estimate the regression equation (copy and paste your output).

c) What is the correlation coefficient?

d) What is the coefficient of determination and how do you interpret it?

Answer 1

(a) from scatterplot diagram we can conclude that the there is positive relationship between year of schooling and salary. And we can say that one with high year of schooling are expected to be high salary.

(b) thus the regression equation is

SALARY hat = 15010.2 +2825.0696552 year of schooling hat

(c) the multiple R given in the regression analysis is the correlation coefficient which is given to be 0.97565

(d) The coefficient of determination is the R² wbich is 0.95189 in the given case.

Coefficient of determination tells that proportion of variation in independent variable  depicted by the dependent variable or how much of the variation in independent variable has been explained by the. Dependent variable.