1) Construct a scatter plot of retention rate against wage and examine the trend; does this support the assumption of a linear model between personnel retention rate and wage? 2) Calculate the...

ENG 2030M Engineering Statistics Week8: Linear Regression Analysis Dr F. Campean Class Exercise Table below presents the results of a staff retention survey across a range of manufacturing companies, reporting the standard hourly rates for pay and the retention of staff expressed as a percentage. Tasks: 1) Construct a scatter plot of retention rate against wage and examine the trend; does this support the assumption of a linear model between personnel retention rate and wage? 2) Calculate the correlation coefficient between the 2 variables; does this confirm your assumptions from task 1? 3) Estimate regression coefficients for a linear model relating the retention rate to the wage; 4) Use your regression model to calculate residuals (errors) between the observed values and fitted values from your model. Construct a run chart of residuals and discuss your findings; 5) Examine the Minitab output for regression analysis on this data. Complete the missing values (calculate and fill in the boxes) and explain /interpret these results. Solution Task 1 Use the box to construct the scatter plot. Interpretation: _________________________________ _________________________________ Task 2 Correlation coefficient r is xx yy xyS S S r · = . Use the results in the table on the back of the page to calculate relevant sums. Sxy = S(xy) -n·Xbar·Ybar = ___________; Sxx = S(x2) -n·Xbar2 = _____________; Syy = S(y2) -n·Ybar2 = ____________ xx yy xyS S S r · = = ___________; Interpretation: _____________________________________________________________________ Task 3 Using the notation y = b0 + b1x xx xy 1 SS b ˆ = = ______________; x b ˆ y b ˆ 0 = - 1 · =________________. Task 4 Use the table on the back of this page to calculate fitted Y (fitted y = b0 + b1x) and residuals. 6.5 7.0 7.5 8.0 8.5 9 65 60 55 75 70 Salary [£ /hr] Staff Retention Rate [%] Wages [£ /hr] Retention rate [%] 6.7 59 7.5 64 7.5 67 7.6 66 7.6 67 7.7 65 7.8 67 7.8 68 7.9 69 8 71 8.7 72 8.7 72 8.7 72 8.9 72 8.9 73 ENG...