Question

Suppose you fit the first rder mu ple egression model y = po + β1x1 + a. Test Ho βι-o against h, β1 , 0 Use α-D 05 b. Find a 99% confidence interval for P2 interpret the interval 2x2 + ε to n= 25 data points and obtain the prediction equation y = 37.1 + 1.19x1 + 1 3 2 Th° estimated standard deviations ofthe sampling distributions of βι and P2 are 0.23 and 0.18, espec ve y . The test statistic is Round to three decimal places as needed.) The p-value is Round to three decimal places as needed.) the null hypothesis. Theresuflicient evidence to support the alternative hypothesis. b. What Is the confldence interval? ound to three decimal places as naeded) Interpret this interval we are ]%confident that the rue value of P2 les in this interval Type a whole number.)

Answer 1

a) To test
Но : 31-0
against $H_1:\beta_1 \neq 0$

Here,

$\hat{\beta_1} = 1.19, SE(\hat{\beta_1}) = 0.23, n = 25$

The test statistic can be written as

which under H₀ follows a t distribution with n-3 df.

52. SE(1

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic

and P-value =

Since P-value < 0.05, so we reject the null hypothesis. There is enough evidence to support the alternative hypothesis.

b) a 99% confidence interval for $\beta_2$

(β2-t0.005,n-3 * SE(32), B2 + t0.005,n-3 * SE(32) )

$=(0.792623,1.80738)$

We are 99% confident that the true value of $\beta_2$ lies in the interval.