Question

correlations and linear regression education and income

3. Use the following data set and complete the table. (Income is the dependent variable and education is the independent variable) Education (Years) I x -* Yi- } (x; - x)(y;-)) (x; -x² Income ($1000) 15 46 13 17 58 46 13 10 40 63 15 18 11 9 11 15 45 12 50 16 9 14 48 58 14 16 50 11

Answer 1

Here, Income is dependent variable & education is independent Vaniable. So, we plot income on y'axis & education only axis. Laniak independent vaniabe) education depandud Cincomes - 1 (xi-*) (ring)(xi-x) cuinyje 16 46 46 2.55556 3-6111 45 Edvention income (xi) (i) xi-x) (Yeny: 1x = 12.44114 ŷ ²38.5 15 -4.49444 1-23.5 109, 94434 1g. 750469 | 552.25 0.55556 7.5 4.1667 0-308646914 56.25 4.55556 10.5 8 8.83342 20075312091 300.25 0.55556 7.5 14.1667 0.3686 56.25 -2.44449 1.5 - 3.66666 5.975276914 2.25 24.5 62-6122 6.530887 rorous 2436 1.44444 -2.5 2.086406914 6.25 1918 -3.44 444 - 20.5 70.61102 I 11 - 864 1669 1920.25 4.44944 | 6.5 -9.38806 1.086406914 42.25 2.55556 -26.5 -67-72234 6.53 0176914 102.25 us 40-88894 12-64 2006 36 -3.44444 - 2.5 18.6111 11.864 1669 1 6.25 5.5 14.77782 2.418 766 914 90.25 iz 58 0.55556 19.5 10.83342 0.308646914 380.25 14 30 11.55556 -8.5 - 13-22226 2-415166914 | 72.25 -3.44944 - 23+5 80 94934 | 11.864 1669 1 F5 225 13.55556 us 40.88954 12.64 2006) 12.25 -1.44 444 -11.5 16.61106 2-0964 06914 132.25 Loint) (yi. (xi-x 2 - 2 = 458 = 132.4444444 =4316.5 7 3.55556 14 48 1.55556 15 50 27 Sum

Pres: 2 a celalene x, 7 and the sh de, both of y. = +(8+1341741*-+1671) = 12.99949 . i to reiz to (istastant 27 ) = 38.5 • standan deviable of x= vance) As the sample size l is 18 Small, so we love this formella . en 2 l - 17 h (xi-ah 2√7.79885 a. Standar deriction ofy - Vranica) = 2.791 (cosset up to 3 deind Placs) > VX 1316.5 = 15.935 ( connet upto 3 deinl places 16 claulate the covaniance ? what does this tell us and what does it not teall us? covaniance (8,412 13 14 (xi) (49) 7 18 458 ( From table weget, &2(xi) (4-9) = 458) 2 25.494 (connet upto 3 deined placey . As comaniance is positive so, thenore exists & relationship between incone and education

calalale the connotation ? > conn (x,y) = CON(x,y) ſuks. such 25.494 2.791x 15.925 I 0-58 to high relation between I polsitive So, elation is positive As, compelation is positive income I eduction ice increasing education. income in einemese Son what is the slope? we know the regression equation of you xis ya gt byn (x-7), where, bye is the slope = n. 20.58x 15.935 23-311 2-791 23.311 connect upto 3 dainel plans, What is the y intencept of - the regioession equation ady ons is Tag + syn (nan) puting, the sake y = 38.5 4 2 12.994, Syn = 3.311 = 38.54 3.311 (- 12.444) = 30.5 + 3.311n - 41.202 2 2.702 +3.3 11 Here, the y intencupt = -2-702

What is the equation for the regression eqution for the negression line } g the know, the nexessin line of younis g = gt byn (wenn de putting the schead j = 38.5, n = 1.94 & by n = 3-34 we get, y = -2.402 +3:311 2