Question

The data given below are the ages at inauguration and of death for the presidents of various countries. Use the technology of your choice to complete parts (a) through (d). B Click the icon to view the data. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b) through (d). For the purposes of this regression, let Inauguration be the explanatory variable (x) and let Death be the response variable (y). i Inauguration and Death There is to the data, so it is to carry out a linear regression. b. Compute the coefficient of determination, 2. Select the correct choice below and fill in any answer boxes within your choice. Inauguration Death Inauguration Death O A. 2- (Round to three decimal places as needed.) OB. It is not appropriate to carry out a linear regression. 58 73 c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. Sel OA. % (Round to one decimal place as needed.) OB. It is not appropriate to carry out a linear regression. d. State how useful the regression equation appears to be for making predictions, O A. Moderately useful OB. Extremely useful O C. It is not reasonable to carry out a linear regression. Print Done Click to select your answer.

Answer 1

Answer: The data is given where x is the explanatory variable denoting he ages at inauguration and y be the response variable denoting the death.

The data is plotted and we see that--

a) There is clustering of data in a specific region with no linear structure in the data, so, it is not suitable to carry out a linear regression.

b) The coefficient of determination r² = 0.1245, since it is much less, so it is not appropriate to use a linear regression.

c) The % of variation in the observed values of the response variable that is explained by the linear regression is 12.45%. Since it is the obtained value of r² is 0.1245 and by definition of r² we know that it represents the amount of variation in the observed values of the response variable that is explained by the linear regression.

d) As the % of variation explained by linear regression is only 12.45%, and also on seeing the plotted graph of y against x, we can say that it is not suitable to carry out linear regression.

[The graph and the answer is obtained using R-software. Code and output are attached below.]

R-code:

#x=ages at inauguration y=death
x=c(55,61,56,57,58,56,6,50,66,53,43,64,48,48,63,46,56,46,56,46,51,45,51,57,57,42,45,49,57,46,55,49,59,63,39,57,53,60,69)
y=c(67,90,83,85,73,80,78,79,68,71,53,65,74,64,77,56,66,63,70,49,57,71,67,71,58,60,72,67,75,60,90,63,88,78,46,64,81,93,93)
plot(x,y)
summary(lm(y~x))

Output:

RR Graphics: Device 2 (ACTIVE) 0608 O 70 0 0 60 50 20 30 40 50 60 70

> *-C(55,61, 56, 57, 58, 56, 6, 50, 66,53, 43, 64,18,18,63,46,56,46,56,46,51,45,5 > y*c (67, 90, 83, 85, 73, 80,78, 79,68,71,53, 65, 74,64,77,56,66,63,70, 49, 57, 71, > plot (x, y) > summary (lm (y=x)) Call: lm (formula = y - x) Residuals: Min 1Q Median -19.541 -7.561 -1.814 30 8.302 Max 25.792 Coefficients: Estimate Std. Error t value Pr (>101) (Intercept) 49.7937 9.37795 309 5.42e-06 *** 0.1761 2 94 0.027€ * Signif. codes: Residual standard error on 37 degrees of freedom Multiple R-squared: 0.125, Adjusted Resquared: 0.1009 F-statistic: 5.263 on end 37 D -value: 0.02756