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	9.66	10.00	10.06
x	2.66	2.75	1.83
x2	NA	−0.31	−0.33
x3	NA	NA	0.26
R2	0.810	0.836	0.896
Adjusted R2	0.809	0.833	0.895

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

b. Select the most appropriate model.

• Linear model

• Quadratic model

• Cubic model

Answer 1

Solution :- 2. Güveni The equations ayer 7:9.6672.667 - linear equation, Y: 10.0671834-0.3372+028x3 -cubic equation. 7:10+ 2.757.013182-quadratic equation At a=1 The equations orie. + linear eqvuation. Yo 9.66 +8.66(1) = 9.66+22.66 12.32 Y: 10:06 +1.833-0.33 x 2 +0.86x3 + cubic equatior = 10:06+ 183(1) + 0.330129 +0.296(1)3=11.89 Y=10+2.754-0.31x2 + Quadratic equation = 10 +0.75017 0.31612 = 12.44

. . At vel The equations are linear equation y=10.32. quadratic equation y= 19.44 cubic equation Vo:11.82. At 4:2 The equations are Y= 9.664 266. + linear equation, =9.66+ 26612) =14.98 y=10+2.758 -0.3120 -Quadratic equation =10+2,75()-0.31(0)2 = 14.96 y:10:06+1:8334-0.334Q+0.8683 * cubic equation = 10:06 +183(Q)-0.33(2)2 +0.2612)3 = 14.48 . At 2=2. The equations are linear equation y: 14.98 Quachratic equation Y = 14096 cubic ecjuation y = 14:48

b) o long all The maximum value of Ra among all models is cubic model , Ti cubic as the appropriate modell