Explain the relationship between compensation ($/hour) and union membership. Does this have the relationship you would expect? Interpret the , r, and the results of the hypothesis test.

Step 1: Calculate means Step 2: Calculate Sum of Squares Compens ation Union ($/hour)- Membership (xi - (xi-xbar) - X (%) - - y xi-xbar yi-ybar xbar)^2 (yi-ybar) $ 33.23 9.6 $ (4.07) 0.31 $ 16.59 -1.27275 $ 34.18 10.1 $ (3.13 0.81 $ 9.77 -2.53932 $ 35.99 9.7 $ (1.31) 0.41 $ 1.71 -0.53947 $ 37.39 9.4 $ 0.09 0.11 $ 0.01 0.010371 $ 39.11 8.8 $ 1.81 (0.49) $ 3.27 -0.88222 $ 39.65 9.1 $ 2.35 (0.19) $ 5.51 -0.4401 $ 39.25 9 $ 1.94 (0.29) $ 3.78 -0.5591 $ 39.61 3.6 $ 2.31 (0.69) $ 5.35 - 1.58963 Means $ 37.30 $ 9.29 Squared sums $ 45.99 -7.81222 Step 3: Calculate slope (b1) (recall b1 = SSxy/SSxx) $ (0.17) Step 4: Calculate the intercept (bo) (recall bo = ybar - xbar * b1) $ 15.62 Step 5: Graph the Scatter Plot, include the line of best fit derived in steps 3 and 4 Relationship between Union Membership and Compensation 11 10 Union Membership (%) 'VE:0:16998+. 15,624 Union Membership 00 60 R2 = 0.7503 (%)- y $32.00 $36.00 $38.00 $40.00 . . . . . .. .. Linear ( Union $34.00 Membership (%)-- y) Compensation ($/hour) Step 6: Determine the goodness of fit of the regression line by calculating SSR, SSE and SSTStep 6: Determine the goodness of fit of the regression line by calculating SSR, SSE and SST Compens ation ($/hour)- yhat = (yhat- (yi- - X bo+bix yhat-ybar ybar)^2 yi-yhat yhat)^2 $ 33.23 $ 9.98 $ 0.69 $ 0.48 $ (0.38) $ 0.14 $ 34.18 $ 9.82 $ 0.53 $ 0.28 $ 0.28 $ 0.08 $ 35.99 $ 9.51 $ 0.22 $ 0.05 $ 0.19 $ 0.04 $ 37.39 $ 9.27 $ (0.02) $ 0.00 $ 0.13 $ 0.02 $ 39.11 $ 8.98 $ (0.31) $ 0.09 $ (0.18) $ 0.03 $ 39.65 $ 8.89 $ (0.40) $ 0.16 $ 0.21 $ 0.04 $ 39.25 $ 8.96 $ (0.33) $ 0.11 $ 0.04 $ 0.00 $ 39.61 $ 8.89 $ (0.39) $ 0.15 $ (0.29) $ 0.09 SSR $ 1.33 SSE $ 0.44 Step 7: Calculate the coefficient of determination R^2 (recall R^2 = SSR/SST) 0.75 Step 8: Calculate the correlation coefficient r (recall r = sign of b1* sqrt(R^2)) $ (0.15) Step 9: Do a hypothesis test for your slope coefficient df 6 hint: n-2 MSE 0.07360095 hint: SSE/df S 0.27129495 hint: sqrt(MSE) s(b1) 0.040006116 hint: s/sqrt(SSxx) t -4.246365407 hint: b1/s(b1) t crit (0.025) Decision? Do Not Reject hint: reject if abs(tstat) >/= t crit