Question

The percent of female wage and salary workers who are paid hourly wages for the years 1979 to 1992. (1989) Year 1979 1980 1981 1982 1983 1984 1985 1986 1987 1990 1992 Percent of workers paid hourly rates 61.2 60.7 61.3 61.3 61.8 61.7 61.8 62.0 62.9 62.8 62.9 e. a. Define the Independent and Dependent variables b. Plot the points on a graph and label the axes c. Write the regression equation. Use correct notation. d. Perform a hypothesis test to determine if there is significant linear correlation. Be sure to include 2 separate conclusions as shown on the lecture notes. Find the expected predicted value given the input value. This is the number written in parenthesis next to the assignment. For example, for #2 find the predicted welfare family size in the year 1980. Answer parts (f) and (g) only if there is significant linear correlation. f. Determine if there are any outliers by graphing. Include the graph with the boundary lines and label the lines. Give the outliers. g. Interpret the slope of the regression line.

Answer 1

ANSWER:

(क) here dependent variable =y= percent of workers Paid hourly rates Independent variable Exo Year Po+ scale on X anisa 1cm= 1 year on y qtis= icm=0.5 63 0 62.5 62 . 0 61.5 0 00 60 60.5 60 198 (920 1482 h) 1986 1988 1992 bb * १९१० Gls ()

regression equation fer nimated) = Intercert زم o thit where h f= slope bo= 9 = b 4 6 = correy vas(X) ple Exi nese na ll a[1979 + 1980+ +1992) = 21829 1984.4 14

+ 62-9) 680-4 9 = Eyj = [61-2660.4+ 11 11 61.8545 E174= E = ( (197934 +(1989€ -t (1992137 11 = 96 43318825 = 3938075 ll varin) = E1724- (E())} = 3938075-61984.4852 varit) € 16.672437 EIRS= {4,2 [ 612)2+(60.75? + f (62 (62-932) ད། 42091.34 Il 3826.485

varty) - Ely - ((y) = 38 26436 _ (c).894) 0.5504 E Cov() EN) - ( E(4) 티깨 음3 2(C14 49 462) 4 (1980 + 604) † - ( 442 4 62-42] 135025) - 12246.09) CyY) Ely) - E() ETH) ㅌ 2리라라 야 20812923 C 0.1631 I. 61203

be = 61185455 - 10.1687 * 1984.455) = -272.927 cos -272-927 + 10.687 **) correlation test (n) To Test: Hoi s=0 H! 140 Test statistic ta & Sn-2 51-82 here corle y Svarlt) Srasly) 20812227 16:6727 # 30.5507 r=0.9282

J 1-10.928232 ith 7 tk/ 210f ta (0.9282) +59 2-7846 7.483 0.3720 here df-n-2 df L 2.262 Decision : we reject Ho at find) $100% level of significance. if it > taizidf, henre we reject Ho 50.059 conclusion there is a correlation between k 4 y. and it is significant.

It is significant L=0.05 Assume p value fer L=0.05 0.000038 for type I emar d =0.05 and C 0.95 It is also Type 7 error = r-la significant because P value ca & ß value e expected predicted value = = @o tbox x = 1980 predicts = -272.927 # 10.1687 * 1980) = 61.0997.

o there is no outlier because there in positive & strong relationship between x4y. Interpretahon of slope! X value increases here is Positive estimated or predict value increases that is more effect on å