Question

y	x	xy	xx	yy
11.4	0	0	0	129.96
11.9	1	11.9	1	141.61
7.1	2	14.2	4	50.41
14.2	3	42.6	9	201.64
5.9	4	23.6	16	34.81
6.1	5	30.5	25	37.21
5.4	6	32.4	36	29.16
3.1	7	21.7	49	9.61
5.7	8	45.6	64	32.49
4.4	9	39.6	81	19.36
4	10	40	100	16
2.8	11	30.8	121	7.84
2.6	12	31.2	144	6.76
2.4	13	31.2	169	5.76
5.2	14	72.8	196	27.04
2	15	30	225	4
94.2	120	498.1	1240	753.66

a. Graph and plot the 16 points (Use the blank graph on the next page of this test).  

 

b. Use the graph to estimate the Y intercept value                     Y Intercept = ___________     

c. Use the graph to estimate Y if X = 3.5                                   Y Estimate = ___________    

d. Calculate SS_xy (4 Points)

Answer 1

a)

b)

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
0	11.4	56.25	30.39	-41.34
1	11.9	42.25	36.15	-39.08
2	7.1	30.25	1.47	-6.67
3	14.2	20.25	69.10	-37.41
4	5.9	12.25	0.00	-0.04
5	6.1	6.25	0.05	-0.53
6	5.4	2.25	0.24	0.73
7	3.1	0.25	7.77	1.39
8	5.7	0.25	0.04	-0.09
9	4.4	2.25	2.21	-2.23
10	4	6.25	3.56	-4.72
11	2.8	12.25	9.53	-10.81
12	2.6	20.25	10.81	-14.79
13	2.4	30.25	12.16	-19.18
14	5.2	42.25	0.47	-4.47
15	2	56.25	15.11	-29.16

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	120	94.2	340	199.1	-208.40
mean	7.50	5.89	SSxx	SSyy	SSxy

sample size ,   n =   16          
here, x̅ = Σx / n=   7.50   ,     ȳ = Σy/n =   5.89  
                  
SSxx =    Σ(x-x̅)² =    340.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   -208.4         
                  
estimated slope , ß1 = SSxy/SSxx =   -208.4   /   340.000   =   -0.6129
                  
intercept,   ß0 = y̅-ß1* x̄ =   10.4846         
                  
so, regression line is   Ŷ =   10.4846   +   -0.6129   *x

                  
Predicted Y at X=   3.5   is                  
Ŷ =   10.48456   +   -0.612941   *   3.5   =   8.339