Question

dentifying the Line of Best Fit (Least Squares Regression)

Question

A random sample of 11 workers produced the following data, where x is the years of employment, and y is the average number of minutes required to complete the morning duties. The data are presented below in the table of values.

x	y
5	49
8	42
10	41
12	39
15	37
16	34
19	30
22	25
25	24
27	22
28	16

What is the equation of the regression line?

Select the correct answer below:

yˆ=10.082x+54.2

yˆ=−1.267x+17.0

yˆ=−1.267x+54.2

yˆ=10.082x+17.0

Answer 1

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
5	49	144.00	267.8	-196.4
8	42	81.00	87.7	-84.3
10	41	49.00	70.0	-58.5
12	39	25.00	40.5	-31.8
15	37	4.00	19.0	-8.7
16	34	1.00	1.9	-1.4
19	30	4.0	7.0	-5.3
22	25	25.00	58.3	-38.2
25	24	64.00	74.6	-69.1
27	22	100.00	113.1	-106.4
28	16	121.00	276.77	-183.00

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	187	359	618.000	1016.5	-783
mean	17.00	32.64	SSxx	SSyy	SSxy

sample size ,   n =   11          
here, x̅ =   17.00   ,   ȳ =   32.6363
                  
SSxx =    Σ(x-x̅)² =    618.00          
SSxy=   Σ(x-x̅)(y-ȳ) =   -783.0          
                  
slope ,    ß1 = SSxy/SSxx =   -1.2670          
                  
intercept,   ß0 = y̅-ß1* x̄ =   54.1752          
                  
so, regression line is   Ŷ =   −1.267x + 54.2