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 2988 30.15 21.07 28.94 15.46 25.14 12.28 21.77 22.71 25.10 16.25 26.02 16.26 2592 15.64 2353 21.50 10 26.83 21.23 7.96 11 25.78 1657 12 24.47 26.41 here for the Excel Data File a.1 . Estimate y! 0 + 5K 1-1+ (Round your answers to 4 decimal places.) a 2. Estimate y-A + 5K '-1 + ,x ,-z+ 1, (Round your answers to 4 decimal places.) b. Use the appropriate model to make a one-step-ahead forecast (t 13) for y (Round intermediate calculations to 4 decimal place s and final answer to 2 decimai places.) y-forecast O Type here to search

Explanation / Answer

Here the regression output is for problem 1 is

so , yt = 18.3466 + 0.3918 xt -1

(b) Here regression output for question 2 is

y^ = 15.06652 + 0.3525 xt-1 + 0.2067 xt -2

Here the model 2 is a better estimate as for the forecast for 13th month

y^(13) = 15.06652 + 0.3525 * 26.41 + 0.2067 * 16.57 = 27.8011 or 27.80

SUMMARY OUTPUT Regression Statistics Multiple R 0.822001 R Square 0.675686 Adjusted R Square 0.639651 Standard Error 1.394852 Observations 11 ANOVA df SS MS F Regression 1 36.48194 36.48194 18.75087 Residual 9 17.51052 1.945613 Total 10 53.99245 Coefficients Standard Error t Stat P-value Intercept 18.34661 1.768823 10.37222 2.64E-06 X Variable 1 0.391847 0.090491 4.330228 0.001904

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