This part of today\'s lab will look at farm populations in the United States dur

Question

This part of today's lab will look at farm populations in the United States during the 20th century. The table below gives data on the number of people living on farms (in millions) in the U.S. throughout various years in the 20th century. x Year|1935-1940 1945|19501 1955 1960 1965 1970 1975 19801 1990 | v Pop. 32.1 30.5 244 23.0 19.1 15.6 124 9.7 8.9 7.2 3.9 regression ino-= 1.255-0.51091x 5. Now that we have a regression line, we can use it to make predictions about the farm population in various years, including years besides those we measured. Note that when you are making predictions below, you can use either the line from. #3 or the line from #4-they should both give the exact same predictions. a) Using the best fitting line, what is the estimate for the population of farmers in the U.S. in 1965 (a year in the data set)? 12.4 b) The year 1965 was included in the data set. What is the residual for this case? egane peidua c) Using the best fitting line, what is the estimate for the population of farmers in the U.S. in 1985 (a year missing from the data set)? d) Do you think your predction from part c above is valid? Why/why not? e) Using the best fitting line, what is the estimate for the population of farmers in the U.S. in 2015 (a year beyond the edge of the data set)? f) Do you think your prediction from part e is valid? Why/why not?

Explanation / Answer

5:

Following is the output of regression analysis assuming 1935 as base year. That is 1935 as 0.

So regression equation is:

y' = 30.75368 - 2.70519x

(A)

For 1965, x = 6 so estimated value is

y' = 30.75368 - 2.70519 * 6 = 14.52254

So predicted value is 14.5

(B)

Residual: 12.4 - 14.5 = -2.1

That ia residual is negative.

(C)

For 1985, x = 10 so estimated value is

y' = 30.75368 - 2.70519 * 10 =3.70178

So predicted value is 3.7.

(D)

Yes it is meaning full. Because 1985 lies in the range of X used for regression model.

(E)

For 2015, x = 16 so estimated value is

y' = 30.75368 - 2.70519 * 16 =-12.52936

So predicted value is -12.5.

(f)

No it is meaning less. Because 2015 does not lie in the range of X used for regression model.

SUMMARY OUTPUT Regression Statistics Multiple R 0.983316916 R Square 0.966912158 Adjusted R Square 0.963235731 Standard Error 1.834198702 Observations 11 ANOVA df SS MS F Significance F Regression 1 884.8177997 884.8178 263.0032 5.7181E-08 Residual 9 30.27856391 3.364285 Total 10 915.0963636 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 30.75368421 1.013406249 30.34685 2.24E-10 28.46120001 33.04616841 X Variable 1 -2.70518797 0.166808011 -16.2174 5.72E-08 -3.082533906 -2.327842034

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