3 Average Age and Length of Service The data show the average ages and lengths of service in months.25.127.125.2 25.8 2770.1 7466.58982AgeTimeSend data to ExcelThe correlation coefficient for the data is r=0.946 and a=0.05. Should regression analysis be done?The regression analysis should not be done.O The regression analysis should be done.Find the equation of the regression line. Round the coefficients to at least three decimal places.'=a+bxa =b =If a service person is 26.5 years old, predict the time that the person will serve. Round the answer to at least onedecimal place.The service person will serve months.X

The equation of the regression line is , y' = a + bx Where , b is slope of regression line. b = n∑xy-∑x∑yn∑x2-∑x2 a is the y-intercept. a = ∑yn-b×∑xnGiven , r = 0.946 , it represent there is linear relationship between average age and length of service. So, the regression analysis should be done. Let , x be the average age ( independent variable ) y be the length of service. ( Dependent variable ) Calculation : We got , ∑x = 130.2 , ∑y = 381.6 , ∑xy = 9970.07 , ∑x2= 3394.1 , ∑y2 = 29457.26, n = 5 Slope : b = n∑xy-∑x∑yn∑x2-∑x2 b = 5*9970.07-130.2381.65*3394.1-1302 b = 8.99404 y-intercept : a = ∑yn-b×∑xn a = 381.65-8.99404×130.25 a= -157.8848We have to find time that the person will serve for 26.5 years old person. The equation of the regression line is , y' = a + bx We got , a = -157.8847 and b = 8.99404 So regression equation is , y' = -157.8847 + 8.99404x put x = 26.5 in above equation y' = -157.8847 + 8.99404*26.5 y'=80.5 The service person will serve 80.5 months