For a sample of 8 employees, a personnel director has collected the following data on ownership of company stock, y, versus years with the firm, x.

X | 6 | 12 | 14 | 6 | 9 | 13 | 15 | 9 |

Y | 300 | 408 | 560 | 252 | 288 | 650 | 630 | 522 |

(a) Determine the least-squares regression line and** interpret** its slope

(b) For an employee who has been with the firm 10 years, what is the predicted number of shares owned?

(c) Is there a statistical significance between years of service and ownership of company stocks? (use α=0.05α=0.05)

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Step 1Given,For a sample of 8 employees, a personnel director has collected the following data on ownership of company stock, y, versus years with the firm, x.X612146913159Y300408560252288650630522Step 2a)Software procedure for regression in Excel.Enter the given data in EXCEL sheet.Go to Data > Data Analysis > Regression.Select x and y ranges with labels.Click OK.  The output obtained from Excel is given below.SUMMARY OUTPUTANOVAFrom the above output,The regression line is obtained as followsY=44.3139+38.7558(x)Interpretation:The y-intercept b0 is the mean value of y when X=0 and the slope b1 is the expected chance in the variable Y with respect to per unit change in variable X.The slope b1 can be interpreted as that for every additional number of year the mean of company stock is predicted to increases by 38.7558 shares.Step 3b)For an employee who has been with the firm 10 years, then their the predicted number of shares owned is calculated as follows:Y=44.3139+38.7558(x)=44.3139+38.7558(10)=44.3139+387.558=431.8719=432For an employee who has been with the firm 10 years, then their the predicted number of shares owned is 432.Step 4c)The hypotheses are given below:Null hypothesis:H0: ρ= 0There is no statistical significance between years of service and ownership of company stocksAlternative hypothesis:Ha: ρ ≠ 0.There is statistical significance between years of service and ownership of company stocks Degrees of freedom:The formula for degrees of freedom is as follows:Df = n – 2.The number of data values given are 5, that is n = 5.Df = n – 2 = 8– 2 = 6. Test Statistic:The test statistic for hypothesis test is calculated as follows:from the above output r=0.8486t=rn-21-r2=0.84868-21-0.8486=2.449test statistic value is 2.449.Step 5Computation of P-value:The tailed P-value for the t-test at 6 degrees of freedom is approximately 0.0498 which can be obtained using the excel formula, “=T.DIST.2T(2.449,6)”. Decision rule:If p-value ≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis.Conclusion:Here, p-value (0.0498) is less than the level of significance (0.05).Therefore, reject the null hypothesis.Thus, there is statistical significance between years of service and ownership of company stocks  ...