Use the technology of your choice to do the following tasks. From the International Data Base, published by the U.S. Census Bureau, we obtained data o

melodykap 2021-02-16 Answered
Use the technology of your choice to do the following tasks. From the International Data Base, published by the U.S. Census Bureau, we obtained data on infant mortality rate (IMR) and life expectancy (LE), in years, for a sample of 60 countries. a) Construct and interpret a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation. d) Make the indicated predictions. e) Compute and interpret the correlation coefficient. f) Identify potential outliers and influential observations.
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estenutC
Answered 2021-02-17 Author has 81 answers

Given: n=Sample size=60 a) IMR is on the horizontal axis and LE is on the vertical axis. image b) When there is no strong curvature presents in the scatterplot, then it is safe to assume that there is a linear relationship between the variables and thus it is then reasonable to find a regression line. We note that the scatterplot of part (a) does not contain strong curvature and thus is reasonable to find the regression line. c) We determine all necessary sums:  xi=1743.1
 yi=4147.6
 xi yi=106485.62
 xi2=90242.13
 yi2=293216.68 Next, we can determine Sxx and Sxy
Sxx=  xi2=90242.13  1743.1260=39602.1698
Sxy=  xi yi  ( xi) ( yi)n=106485.62  1743.1  4147.660= 14009.0727 The estimate b of the slope β is the ratio of Sxy and Sxx:
b= SxySxx= 14009.072739602.1698= 0.3537 The mean is the sum of all values divided by the number of values: x=  xin= 1743.160=29.0517
y=  yi}{n}= 4147.660=69.1267 The estimate a of the intercept α is the average of y decresed by the product of the estimate of the slope and the average of x
a= y  bx=69.1267  (0.3537)  29.0517=79.4036 General least-squares equation: y^= α + β x. Replace α by a=79.4036 and β by b= 0.3537 in the general least-squres equation
y^=a + bx=79.4036  0.3537x
image d) Let us evalute the regression line in part (c) at x=30:

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