A manager wishes to determine the relationship between the number of years her sales representatives have been employed by the firm and their amount of sales (in thousands of dollars) per month. Find the equation of the regression line for the given data. A manager wishes to determine the relationship between the number of years her sales representatives have been employed by the firm and their amount of sales (inthousands of dollars) per month. Find the equation of the regression line for the given data.Years of employed (x)31078153111Sales (y)313378626570485564(a) Find the correlation coefficient(Round your answer to nearest thousandth)(b) Find the critical value(c) Find the equation of least square regression.y =(Round slope and intercept to nearest thousandth)(d) What would be the predicted sales if the sales representative was employed by the firm for 20 years.$(Round your answer to nearest $. ) Example) If your answer is 125.21, input as 125.(e) Find the residual when the sales representative was employed by the firm for 15 years.Round your answer to nearest thousandth.

Given : Number of years her sales representatives have been employed by the firm and their amount of sales (in thousands of dollars) per month. Years of employed (x) Sales (y) x2 y2 x×y 2 31 4 961 62 3 33 9 1089 99 10 78 100 6084 780 7 62 49 3844 434 8 65 64 4225 520 15 70 225 4900 1050 3 48 9 2304 144 1 55 1 3025 55 11 64 121 4096 704 ∑xi = 60 ∑yi = 506 ∑xi2 = 582 ∑yi2 =30528 ∑xi×yi =3848a) Sample size, n = 9 Correlation coefficient, r = n×∑x×y-∑x×∑yn×∑x2-∑x2×n×∑y2-∑y2 Correlation coefficient, r = 9×3848-60×5069×582-602×9×30528-5062 Correlation coefficient, r = 34632-3036040.4722×136.8064 Correlation coefficient, r = 42725536.859 Correlation coefficient, r = 0.7716 b) DF = n - 2 = 9 - 2 = 7 critical value, t0.05, 7 = 1.895c) Regression line : y^ =m×x+b m= n×∑x×y-∑x×∑yn×∑x2-∑x2 m= 9×3848-60×5069×582-602 m= 42721638 m= 2.608 b = y¯ -m×x¯ b = 5069-2.608×609 b = 38.835 y^ =2.608×x+38.835d) Predicted sales if the sales representative was empolyed by the firm for 20 years. x = 20 y^ =2.608×x+38.835 y^ =2.608×20+38.835 y^ =90.995 Hence, Predicted sales if the sales representative was empolyed by the firm for 20 years is 90.995. e) residual when the sales representative was employed by the firm for 15 years. y^ =2.608×x+38.835 y^ =2.608×15+38.835 y^ =77.955 Residual = y - y^ = 70 - 77.955 Residual = y - y^ = 70 - 77.955 = -7.955 Hence, residual when the sales representative was employed by the firm for 15 years is -7.955.