2 (Applications) (60 points) Suppose that you've been hired as a business analyst by a consumer...

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2 (Applications) (60 points) Suppose that you've been hired as a business analyst by a consumer products manufactur- ing company. The company assembles electric scooters at the company's production facility. The production facility is set up in a way which enables the workers to work independently from one another, so that each worker can work any amount of hours without affecting the productivity of other workers. You observe the following data relating to five assembly work- ers. The dataset includes the amount of time each worker spent assembling scooters during the past week (X;), in hours, and the number of scooters that they've completed during that week (Yi). Worker # (i) Scooters made (Y;) | Hours worked (X;) 1 2 X = 22 X2=28 X3 = 34 Y = 52 Y = 63 Y3 = 79 Y = 92 X = 40 5 Y = 103 X5 = 45 234 NO Suppose you adopt the following linear regression model to assess worker efficiency: Y = + Xi l (1) and estimate coefficients using OLS and the data above to obtain the following estimates: Estimate St. Deviation 1.4489 31 2.2589 2.2487 0.0647 Table 1: OLS estimates of the coefficients from model (1). (a) (7 points) Interpret the estimates above. What can we learn about the relationship between hours worked (X;) and the number of scooters produced (Y;) based on the estimates B and B? (b) (8 points) Using the estimates from Table 1, test whether the intercept term in this model is statistically-significant. Formulate the appropriate hypothesis and test it at a = 5% level of significance. How would you interpret your test result? Are you surprised by the result? 2 (Applications) (60 points) Suppose that you've been hired as a business analyst by a consumer products manufactur- ing company. The company assembles electric scooters at the company's production facility. The production facility is set up in a way which enables the workers to work independently from one another, so that each worker can work any amount of hours without affecting the productivity of other workers. You observe the following data relating to five assembly work- ers. The dataset includes the amount of time each worker spent assembling scooters during the past week (X;), in hours, and the number of scooters that they've completed during that week (Yi). Worker # (i) Scooters made (Y;) | Hours worked (X;) 1 2 X = 22 X2=28 X3 = 34 Y = 52 Y = 63 Y3 = 79 Y = 92 X = 40 5 Y = 103 X5 = 45 234 NO Suppose you adopt the following linear regression model to assess worker efficiency: Y = + Xi l (1) and estimate coefficients using OLS and the data above to obtain the following estimates: Estimate St. Deviation 1.4489 31 2.2589 2.2487 0.0647 Table 1: OLS estimates of the coefficients from model (1). (a) (7 points) Interpret the estimates above. What can we learn about the relationship between hours worked (X;) and the number of scooters produced (Y;) based on the estimates B and B? (b) (8 points) Using the estimates from Table 1, test whether the intercept term in this model is statistically-significant. Formulate the appropriate hypothesis and test it at a = 5% level of significance. How would you interpret your test result? Are you surprised by the result?