Question

Salesperson	Years of Experience	Annual Sales ($1000s)
1	1	85
2	4	100
3	4	91
4	4	97
5	6	107
6	9	109
7	10	118
8	11	126
9	10	113
10	14	132

• Compute b₁ and b₀ (to 1 decimal).

  b₁ =

  b₀ =

  Complete the estimated regression equation (to 1 decimal).

  y = ... + x

• According to this model, what is the change in annual sales ($1000s) for every year of experience (to 1 decimal)?

• Compute the coefficient of determination (to 3 decimals). Note: report r² between 0 and 1.

  r² =

  What percentage of the variation in annual sales ($1000s) can be explained by the years of experience of the salesperson (to 1 decimal)?

  ... %

• A new salesperson joins the team with 6 years of experience. What is the estimated annual sales ($1000s) for the new salesperson (to the nearest whole number)?

  $ ...

Answer 1

	X	Y	X * Y
	1	85	85	1	7225
	4	100	400	16	10000
	4	91	364	16	8281
	4	97	388	16	9409
	6	107	642	36	11449
	9	109	981	81	11881
	10	118	1180	100	13924
	11	126	1386	121	15876
	10	113	1130	100	12769
	14	132	1848	196	17424
Total	73	1078	8404	683	118238

Equation of regression line is


b = 3.6

a =( 1078 - ( 3.5616 * 73 ) ) / 10
a = 81.8

Equation of regression line becomes

b0 = a = 81.8

b1 = b = 3.6

r = 0.969

Coefficient of Determination

Explained variation = 0.938* 100 = 93.8%
Unexplained variation = 1 - 0.938* 100 = 6.2%

When X = 6
= 81.8 + 3.562 X
= 81.8 + 3.562 * 6
= 103