Answer to Question #321153 in Statistics and Probability for oslo

Question

The table below shows data collected in a research on the relationship

between monthly income and monthly expenditure of citizens in town Q.

Use it to answer the following questions.

Earner A B C D E F G H I J

Income usd . 44 65 50 57 96 94 110 34 79 65

Expenditure usd.“ 41 60 40 50 80 68 84 30 55 48

(a) Fit the regression line of expenditure on income using least squares

method.

(b) Using the regression line obtained in (a) above, estimate the expected

amount of expenditure of a Kenyan whose monthly income is usd.

75,000.

Answer 1

^a)

^{x y (x-mean x )(y-mean x)} (xi-mean x)²

^{44 41 (44-69.4)(41-55.6)= 645.16}

^{65 60 (65-69.4)(60-55.6) 19.36}

^{50 40 (50-69.4)(40-55.6) 376.36}

^{57 50 (57-69.4)(50-55.6) 153.76}

^{96 80 (96-69.4)(80-55.6) 707.56}

^{94 68 (94-69.4)(68-55.6) 605.16}

^{110 84 (110-69.4)(84-55.6) 1648.36}

^{34 30 (34-69.4)(30-55.6) 1253.16}

^{79 55 (79-69.4)(55-55.6) 92.16}

^{65 48 (65-69.4)(48-55.6) 19.36}

^{3764.6 5520.4}

^{mean x=}$\frac {\sum xi }{n}$ =69.4

mean y=$\frac{\sum yi}{n}$ =55.6

$\sum (xi-mean x)(yi-mean y)=3764.6$

slope =$\frac {\sum (xi-mean x)(yi-mean y))}{\sum (xi-mean x )^2}$

slope =$\frac{3764.6}{5520.4}$ =0.6819

y intercept =mean y-slope$\cdot mean x$

y intercept =55.6-0.6819$\cdot69.4$

y intercept =8.2761

the regression

y=8.2761+0.6819x

b)

when =75000

y=8.2761+0.6819$\cdot$75000

y=51150.78