Question

You ask 6 of your friends how many dogs they have and how many cats they have. You record the data as ordered pairs (0,0), (0,1), (1,1), (2,1), (3,3), (5, 4).

1.Create a scatter plot of the data

2.Draw in an estimate of the least squares regression

3.Calculate the least squares regression line. Write the equation of that line.

Answer 1

1)

2)

3)

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
0	0	3.36	2.78	3.06
0	1	3.36	0.44	1.22
1	1	0.69	0.44	0.56
2	1	0.03	0.44	-0.11
3	3	1.36	1.78	1.56
5	4	10.03	5.44	7.39

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	11	10	18.83333333	11.3	13.67
mean	1.83	1.67	SSxx	SSyy	SSxy

sample size ,   n =   6          
here, x̅ = Σx / n=   1.83   ,     ȳ = Σy/n =   1.67  
                  
SSxx =    Σ(x-x̅)² =    18.8333          
SSxy=   Σ(x-x̅)(y-ȳ) =   13.7          
                  
estimated slope , ß1 = SSxy/SSxx =   13.7   /   18.833   =   0.7257
                  
intercept,   ß0 = y̅-ß1* x̄ =   0.3363          
                  
so, regression line is   Ŷ =   0.3363   +   0.7257   *x