Question

Using the data set from the previous question (scatterplot.xlsx).

With the data point with the smallest x value removed, the scatter plot now suggests a ________   ["nonlinear" OR "linear"]         relationship between the dependent and independent variables.

Data:

x	y
45	2358
56	4204
26	287
54	3849
24	925
23	3273
34	-678
45	3748
47	2898
43	1974
32	226

Answer 1

With the data point with the smallest x value removed, the scatter plot now suggests a linear  relationship between the dependent and independent variables.

Line of Regression Y on X i.e Y = bo + b1 X
X	Y	(Xi - Mean)^2	(Yi - Mean)^2	(Xi-Mean)*(Yi-Mean)
45	2358	36	68263.424	1567.636
56	4204	289	4440598.232	35823.636
26	287	169	3275112.9	23526.455
54	3849	225	3070459.615	26284.091
24	925	225	1372944.866	17575.91
23	3273	256	1383617.465	-18820.363
34	-678	25	7699111.589	13873.637
45	3748	36	2726701.53	9907.636
47	2898	64	642037.94	6410.182
43	1974	16	15061.99	-490.909
32	226	49	3499620.631	13095.091

calculation procedure for regression
mean of X = ∑ X / n = 39
mean of Y = ∑ Y / n = 2096.7273
∑ (Xi - Mean)^2 = 1390
∑ (Yi - Mean)^2 = 28193530.18
∑ (Xi-Mean)*(Yi-Mean) = 128753.002
b1 = ∑ (Xi-Mean)*(Yi-Mean) / ∑ (Xi - Mean)^2
= 128753.002 / 1390
= 92.628
bo = ∑ Y / n - b1 * ∑ X / n
bo = 2096.7273 - 92.628*39 = -1515.767
value of regression equation is, Y = bo + b1 X
Y'=-1515.767+92.628* X