Question

Stat 3309 - Statistical Analysis for Business Applications I Consider the following data representing the starting salary in $1,000) at some company and years of prior working experience in the same field. The sample of 10 employees was taken and the following data is reported. years of experience starting salary in $1,000) 2 50 15 18 20 Part 1: Use the formulas provided on the 3rd formula sheet to compute the following quantities. Open an Excel spreadsheet and write the table with data given above. Add columns for r, yº, and ry, as well as the last row for . For each of the following quantities, write the formula for it in a cell and evaluate it. (a) Find the sample correlation coefficient r. (b) Find the slope by of the sample regression line. (c) Find the y-intercept bo of the sample regression line. (d) What is the equation of the sample regression line? (e) Find the predicted starting salary for a person who spent 15 years working in the same field. (f) Find the observed starting salary for a person who spent 15 years working in the same field. (g) What is the difference between the observed and the predicted starting salary for a person who spent 15 years working in the same field? (h) Find the total sum of squares SST. (i) Find the sum of squares error SSE. (j) Find the sum of squares regression SSR. (k) Use the answers from (h)-() to confirm that SST = SSR + SSE. (1) Find the coefficient of determination R. (m) Use your answers for (a), (b) and (1), to confirm that r= VRP. (n) What proportion of variation is explained using the regression model? o) Find the standard error of the estimate se (p) Find the standard error of the regression slope Sb. (q) Does the number of years of prior working experience in the same field affect the starting salary at this company ? Use the sample provided above and the significance level of 0.05.

Please answer all the questions relating to part 1

Answer 1

(a) The sample correlation coefficient, r, is 0.985.

(b) The slope, b1, of the regression line, is 2.1322.

(c) The y-intercept, bo, of the regression line, is 45.4177.

(d) The equation of the regression line is:

y = 45.4177 + 2.1322*x

years of experience	starting salary
0	45
2	50
5	55
7	62
8	63
10	70
12	68
15	75
18	81
20	92
	r²	0.971
	r	0.985
	Std. Error	2.579
	n	10
	k	1
	Dep. Var.	starting salary
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,791.688	1	1,791.688	269.36	1.91E-07
Residual	53.2124	8	6.6515
Total	1,844.900	9
Regression output				confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	45.4177
years of experience	2.1322	0.1299	16.412	1.91E-07	1.8326	2.4318

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