Consider the following 10 observations on the response varia

Consider the following 10 observations on the response variable y and the explanatory variable x.

Estimate the linear regression model, y = ₀ + ₁x + . (Round your answers to 4 decimal places.)

Estimate the quadratic regression model, y = ₀ + ₁x + ₂x² + . (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)

Use the appropriate numerical measure to justify which model fits the data best.

Given the best-fitting model, predict y for x = 4, 8, and 12. (Round intermediate coefficient values to 4 decimal places and final answers to 2 decimal places.)

Find x at which the quadratic equation reaches a minimum or maximum. (Round intermediate coefficient values to 4 decimal places and final answer to 2 decimal places.)

The (max or min) of the quadratic equation is achieved at x = ___ units.

Solution

From Excel

a) linear regression model, y = 0 + 1x +

The regression model is y hat=13.3087+0.3391(x)

a 2) quadratic regression model, y = 0 + 1x + 2x² + .

From excel

y = 1.7656 + 4.0966x - 0.2528x²

b)

The linear regression model, y = 0 + 1x +

and R² = 0.1317

quadratic regression model, y = 0 + 1x + 2x² + .

R² = 0.5844

From above R², quadratic regression model R² is high hence quadratic regression model is best fits for the given data.

C) Given the best-fitting model, predict y for x = 4, 8, and 12.

The fitted regression model is

y = 1.7656 + 4.0966x - 0.2528x²

when x=4

y = 1.7656 + 4.0966x - 0.2528x²

y= 14.1072

when x=8

y = 1.7656 + 4.0966x - 0.2528x²

y=18.3592

when x=12

y = 1.7656 + 4.0966x - 0.2528x²

y=14.5216