l. use the estimated regression line to predit y when x = 20. n. Construct a 95-

Question

l. use the estimated regression line to predit y when x = 20.

n. Construct a 95-percent confidence interval for B1

o. Test, at the 5-percent level of significance, whether B2 = 2. Clearly state the null and alternative hypothesis, the test statistic and your conclusion.

1. (34 marks) A population is assumed to follow the behaviour y, -B1 B2x e, where B, and ß, are unknown population parameters and e ~ iid N(0,of) ·Use the following sample to answer the following questions. x 1555 43 672944 59 81 61 22 38 | 5201 440 | 210 | 300 | 140 | 95 | 320 | 190 | 200 | 400 | 250

Explanation / Answer

l)

y^ = 383.6938 -2.2483 * x

when x = 20

y^ = 383.6938 -2.2483 *20

= 338.7278

n)

95% confidence interval is (149.0632,618.3245)

o)

TS = (b2^ - 2)/se(b2)

= (-2.2483 - 2)/2.0537

= -2.06860

df = 9, t-critical = 2.262

since |TS| < 2.262

we fail to reject the null hypothesis

SUMMARY OUTPUT Regression Statistics Multiple R 0.342802388 R Square 0.117513477 Adjusted R Square 0.019459419 Standard Error 130.5083736 Observations 11 ANOVA df SS MS F Significance F Regression 1 20412.62515 20412.62515 1.198456031 0.302061406 Residual 9 153291.9203 17032.43559 Total 10 173704.5455 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 383.6938316 103.7198732 3.699328007 0.004925685 149.0631776 618.3244856 x -2.248311571 2.053739912 -1.094740166 0.302061406 -6.894194023 2.39757088

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