Determine the confidence interval for beta₁, predicted value, average value, prediction interval, given x_p

Determining the relationship (if any) between employee age and # of sick days they take Employee age Sick days 30 50 40 6 | 3 55 30 | 7 600 258 Regression Statistics - Multiple R 0.86970 R square 0.75638 Adjusted R2 0.71578 Standard error 1.8344 Observations 8 ANOVA - df F Significant F 0.00500 M S 62.68510 3.36506 Regression Residual Total 18.62822 SS 62.68510 20.19037 82.87547 Coefficients Standard T Stat P-value Lower 95% Upper 95% Error Intercept 13.87553 2 .12866 6.51843 0.00062 8.66689 19.08417 Age -0.22014 0.05101 -4.31562 0.00501 -0.34496 -0.09532 1. Determine 95% confidence interval for B1 (the slope of the line) to three decimal places a. -0.345,-0.095 2. Find predicted value of #sick days an employee will take per year provided they are 41 (one decimal place) a. 4.8 3. Find 95% confidence interval for avg. #sick days/year an employee will take provided they are 41 (two decimal places) a. 3.21, 6.39 4. Suppose a new employee is 41, find a 95% prediction interval for the #sick days this employee will take this year (two decimals) a. 0.04, 9.56 5. Use this model to predict the #sick days per year for an employee who is fifty-one years old (nearest whole integer) a. 3 Simple Linear Regression Model y, = Be + B,x,+; Estimated Simple Linear Regression Equation , = be +b, x; Sum of Squared Errors SSE = E(y 5) = {(y;-(bo+b,x;))? Slope of the Least Squares Line y-Intercept of the Least Squares Line bo = 5 6,5=(. v, -6, x) Mean Square Error 222 =)_sse SSE n-2 n -2 Standard Error 2(y-) SSE n- 2 Vn-2 Total Sum of Squares TSS = E(y; -7) TSS=SSE + SSR Sum of Squares of Regression SSR = TSS-SSE Coefficient of Determination SSR R? - SSR, SSE SSE TSS TSS Sample Estimate of the Variance of b, Sample Estimate of the Standard Deviation (Standard Error) of b, VE(x; -7) 100(1 - a)% Confidence Interval for B bi Ft./2.01 Son Test Statistic for Testing the Hypothesis B, 70 1 = 60 by 100(1-a)% Confidence Interval for the Mean Value of y, given x = Xp: y Eta/25, pevn (x,-F) 100(1-a)% Prediction Interval for the Value of y, given x = Xp: 11 (x,-.7) y Eta/29,1+-+ aze y n. (.x; 7) Multiple Regression Model y; = B. +3,x; + Bxz; +...+ BXxi +8, Estimated Multiple Regression Equation y = b + bx + b,x, ++bx Adjusted RP (n-1 SSE R2 =1-1- (n-k-1) TSS F-Statistic Sum of Squares of Regression F=- Sum of Squared Errors n-(k+1) SSR k Mean Square Regression SSE Mean Square Error n-(k+1) 100(1 - a)% Confidence Interval for Individual Coefficients b; +12/2.df Sb Test Statistic for Testing the Hypothesis 3,60 7 = b;-0 _b Determining the relationship (if any) between employee age and # of sick days they take Employee age Sick days 30 50 40 6 | 3 55 30 | 7 600 258 Regression Statistics - Multiple R 0.86970 R square 0.75638 Adjusted R2 0.71578 Standard error 1.8344 Observations 8 ANOVA - df F Significant F 0.00500 M S 62.68510 3.36506 Regression Residual Total 18.62822 SS 62.68510 20.19037 82.87547 Coefficients Standard T Stat P-value Lower 95% Upper 95% Error Intercept 13.87553 2 .12866 6.51843 0.00062 8.66689 19.08417 Age -0.22014 0.05101 -4.31562 0.00501 -0.34496 -0.09532 1. Determine 95% confidence interval for B1 (the slope of the line) to three decimal places a. -0.345,-0.095 2. Find predicted value of #sick days an employee will take per year provided they are 41 (one decimal place) a. 4.8 3. Find 95% confidence interval for avg. #sick days/year an employee will take provided they are 41 (two decimal places) a. 3.21, 6.39 4. Suppose a new employee is 41, find a 95% prediction interval for the #sick days this employee will take this year (two decimals) a. 0.04, 9.56 5. Use this model to predict the #sick days per year for an employee who is fifty-one years old (nearest whole integer) a. 3 Simple Linear Regression Model y, = Be + B,x,+; Estimated Simple Linear Regression Equation , = be +b, x; Sum of Squared Errors SSE = E(y 5) = {(y;-(bo+b,x;))? Slope of the Least Squares Line y-Intercept of the Least Squares Line bo = 5 6,5=(. v, -6, x) Mean Square Error 222 =)_sse SSE n-2 n -2 Standard Error 2(y-) SSE n- 2 Vn-2 Total Sum of Squares TSS = E(y; -7) TSS=SSE + SSR Sum of Squares of Regression SSR = TSS-SSE Coefficient of Determination SSR R? - SSR, SSE SSE TSS TSS Sample Estimate of the Variance of b, Sample Estimate of the Standard Deviation (Standard Error) of b, VE(x; -7) 100(1 - a)% Confidence Interval for B bi Ft./2.01 Son Test Statistic for Testing the Hypothesis B, 70 1 = 60 by 100(1-a)% Confidence Interval for the Mean Value of y, given x = Xp: y Eta/25, pevn (x,-F) 100(1-a)% Prediction Interval for the Value of y, given x = Xp: 11 (x,-.7) y Eta/29,1+-+ aze y n. (.x; 7) Multiple Regression Model y; = B. +3,x; + Bxz; +...+ BXxi +8, Estimated Multiple Regression Equation y = b + bx + b,x, ++bx Adjusted RP (n-1 SSE R2 =1-1- (n-k-1) TSS F-Statistic Sum of Squares of Regression F=- Sum of Squared Errors n-(k+1) SSR k Mean Square Regression SSE Mean Square Error n-(k+1) 100(1 - a)% Confidence Interval for Individual Coefficients b; +12/2.df Sb Test Statistic for Testing the Hypothesis 3,60 7 = b;-0 _b