Question

Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R² and adjusted R².

	Linear	Quadratic	Cubic
Intercept	9.31	9.64	9.70
x	2.56	2.65	1.76
x2	NA	−0.30	−0.32
x3	NA	NA	0.25
R2	0.782	0.806	0.864
Adjusted R2	0.780	0.803	0.863

a. Predict y for x = 1 and 5 with each of the estimated models. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

	Linear yˆ	Quadratic yˆ	Cubic yˆ
x = 1
x = 5

b. Select the most appropriate model.

• Linear model

• Quadratic model

• Cubic model

Answer 1

a). the predicted values of y be:-

x	linear	quadratic	cubic
1	11.87	11.99	11.39
5	22.11	15.39	41.75

b). the most appropriate model is :-

cubic model

[ because, the adjusted R² for cubic model = 0.863 and R² = 0.864.

which is greater than linear and quadratic model.

we know that the higher the value of R² better is the model.

so, cubic model is the best ]

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