18.(10 points)Suppose you are tasked with analyzing productivity data for a firm that produces outsourced reports for other companies. The first few rows of the data look like this, wherereportsis the number of reports produced in an observed week,num_employeesis the number of employees who worked that week andtotal_employee_hoursis the number of combined hours worked by those employees that week:

reports num_employees 1441 19 1517 16 1385 12 1518 11 2209 19 1384 11

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https://www.coursehero.com/file/82457809/FinalExampdf/

total_employee_hours 543 524 505 521 720 549

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We run a regression on the full dataset and obtain the following output:

Regression Statistics

Multiple R

0.92

R Square

0.84

Adjusted R Square

0.83

Standard Error

150.40

Observations

50

ANOVA

df

SS

MS

F

Significance F

Regression

2

5563450.267

2781725.13

?

2.11241E-19

Residual

47

1063167.413

22620.58

Total

49

6626617.68

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-66.68

126.00

-0.53

0.599127113

-320.15

186.79

num_employees

26.35

10.11

2.61

0.012243379

6.01

46.69

total_employee_hours

2.12

0.20

10.50

6.44059E-14

1.72

2.53

1. Based on the output, how many weeks of data are in our full sample, and how much of the variation in the number of reports produced is explained by the two independent variables (please specify what value you use to estimate the amount of variation explained)?[2 points]
2. Calculate the missing F-statistic in the ANOVA portion of the regression and explain what theSignificance Fvalue tells us about the regression overall.[2 points]
3. What is the equation for this regression model that we would use to produce a point estimate for number of reports produced in a given week in the future? Separately, use the coefficients to predict a point estimate of how many additional reports we would expect to produce, all else equal, if we were to add one more employee working 40 hours that week.[4 points]
4. All else equal, if we were to add one more employee in a given week, what range of additional reports would we expect to produce, with 95% confidence?[2 points]

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