Question

Identify the 9 EVs as either the experimental EVs or observational EVs. Explain.

Problem 12 (18 points): The table below shows the coefficient table for the quadratic regression y = B. + B x + Box +e Estimate Std. Error_t value Pr(lt) (Intercept) 1.2863 7.9286 0.162 0.872 13.4674 3.1313 4.301 8.53e-05 3.9634 0.3069 12.916 <2e-16 Residual standard error: 1.068 on 47 degrees of freedom Multiple R-squared: 0.996, Adjusted R-squared: 0.9959 F-statistic: 5904 on 2 and 47 DF, p-value: <2.2e-16 56.205 -22.121 2.147 with (X'X)"= -22.121 8.766 -0.856 2.147 -0.856 0.084 Suppose we want to estimate the optimal value of x which minimizes the response y (a) (5 points) What is the point estimate of the optimal value of x? (b) [9 points) Approximate the distribution of the point estimate in part (a). (c) [4 points) Construct a 95% CI for the optimal value of x. [CDF of N(0,1): (1.96)-0.975, 0(1.645)=0.95, 0(1.282)=0.90]

Answer 1

A) The point estimate is nothing but the estimated value/coefficient value of x = 13.4674

B) The point estimate which follows Normal distribiution and the point estimate is 13.4674 and standard error is 3.1313

and the p value is less than 0.05. So, it is lineary dependent.

C) The 95% CI for the optimal value of x

the formula is coefficiet of x ± (1.96*standard error of x)

13.4674 ± 6.137348 = (7.33,19.60)

The 95% CI for the optimal value of x = (7.33,19.60)