A publishing company is interested in understanding the relationship between the years of experience of its sales staff and their annual sales. The data they collect from a random sample of 12 sales representatives is reported below. Annual sales ($1,000s) (y) Years of experience (x) 477.26 2.91 458.35 5.2 261.12 2 641 8.08 192.61 1.94 448.8 6.12 349.46 7.35 242.76 1 315.12 4.12 279.76 2.1 641.9 9.09 546.11 6.18 Mean annual sales are $404.52 (in $1,000s) and the mean number of years work experience are 4.67. Linear regression analysis is undertaken using Excel and the output is reported in the following table. SUMMARY OUTPUT Regression Statistics Multiple R 0.82909202 R Square 0.68739358 Adjusted R Square 0.65613294 Standard Error 90.2743705 Observations 12 ANOVA df SS MS F Significance F Regression 1 179199.385 179199.385 21.9891062 0.0008554 Residual 10 81494.6198 8149.46198 Total 11 260694.005 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 184.76 53.62 3.45 0.01 65.28 304.24 Years of Exp (x) 47.02 10.03 4.69 0.00 24.68 69.36 State the linear regression equation for this data and interpret both the intercept and the slope coefficient.
A publishing company is interested in understanding the relationship between the years of experience of its sales staff and their annual sales. The data they collect from a random sample of 12 sales representatives is reported below.
Annual sales ($1,000s) (y)
Years of experience (x)
477.26
2.91
458.35
5.2
261.12
2
641
8.08
192.61
1.94
448.8
6.12
349.46
7.35
242.76
1
315.12
4.12
279.76
2.1
641.9
9.09
546.11
6.18
Mean annual sales are $404.52 (in $1,000s) and the mean number of years work experience are 4.67.
Linear
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.82909202
R Square
0.68739358
Adjusted R Square
0.65613294
Standard Error
90.2743705
Observations
12
ANOVA
df
SS
MS
F
Significance F
Regression
1
179199.385
179199.385
21.9891062
0.0008554
Residual
10
81494.6198
8149.46198
Total
11
260694.005
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
184.76
53.62
3.45
0.01
65.28
304.24
Years of Exp (x)
47.02
10.03
4.69
0.00
24.68
69.36
State the linear regression equation for this data and interpret both the intercept and the slope coefficient.
Linear regression equation :
Intercept = 184.76
Here, when x = 0, the mean value of Annual sales would be 184.76 thousands.
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