Consider the following data on the response variable y and the explanatory varia

Question

Consider the following data on the response variable y and the explanatory variable x. The data are also on the text website, labeled Exercise 18.33 27.9629.88 2 30.15 21.07 28.94 15.46 25.14 12.28 21.77 22.71 6 25.10 16.25 26.02 16.26 25.92 15.64 23.53 21.50 10 26.83 21.23 11 25.78 16 57 12 24.47 26.41 a1. Estimate y-A + ,h-1+ 1 , (Round your answers to 4 decimal places.) 1-1 a2. Estrmate y-A + 1-1 + .x-zt 1 , (Round your answers to 4 decimal places.) orecast b. Use the appropriate model to make a one-step-ahead forecast (t 13) for y. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) y forecast O Type here to search

Explanation / Answer

a)

yt = 18.3466 + 0.3918 * xt-1

b)

yt = 15.0665 + 0.3525 * xt-1 + 0.2067 *xt-2

c)

t = 13

we will use b) model

y13 = 15.0665 + 0.3525 * x12 + 0.2067 *x11

= 15.0665 + 0.3525 * x12 + 0.2067 *x11

= 15.0665 + 0.3525 *26.41 + 0.2067 *16.57

= 27.8010

SUMMARY OUTPUT Regression Statistics Multiple R 0.822001148 R Square 0.675685887 Adjusted R Square 0.639650985 Standard Error 1.394852243 Observations 11 ANOVA df SS MS F Regression 1 36.48193952 36.48193952 18.75087 Residual 9 17.51051502 1.94561278 Total 10 53.99245455 Coefficients Standard Error t Stat P-value Intercept 18.34660    1.76882255 10.37221598 2.64E-06 X Variable 1 0.39184 0.090491135 4.330227905 0.001904

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