Question

A linear regression model takes the pressure level from a production process and uses this to predict product quality in advance of production. This model has already been fitted to the data, and the table below displays predicted values from the model along with the actual values.

Predicted Quality Y^	57	45	64	41
Actual Quality Y	56	64	67	58

Based on the above information, the coefficient of determination is given by:

Answer 1

Solution :

from given information:

S.No		X	(X-x̄)	(X-x̄)2
1		57	5.25	27.5625
2		45	-6.75	45.5625
3		64	12.25	150.0625
4		41	-10.75	115.5625
average xbar =Σx/n		51.75	Σ(X-x̄)2=	338.75

SST =338.75

Y	(y-ybar)	(y-y^)^2
56	-5.25	27.5625
64	2.75	7.5625
67	5.75	33.0625
58	-3.25	10.5625
61.25	total	78.75

SSE =78.75

coefficient of determination =1-SSE/SST =1-78.75/338.75 = 0.7675

Let me know in the comment section if anything is not clear. I will reply ASAP!
If you liked the answer, please give a thumbs-up. This will be quite encouraging for me.Thank-you!