An industrial engineer at a furniture manufacturing plant wishes to investigate how the plant’s electricity usage depends on the amount of the plant’s production. He suspects that there is a simple linear relationship between production measured as the value in million dollar units of furniture produced in that month (x) and the electrical usage in units of kWh (kilowatt-hours, y). The following data were collected

(a) Draw a scatter diagram of these data. Does a straight-line relationship seem plausible?

(b) Fit a simple linear regression model to these data.

(c) Test for significance of regression using 0.05. What is the P-value for this test?

(d) Find a 95% CI estimate on the slope.

(e) Test the hypothesis H0: 1 0 versus H1: 1 0 using 0.05. What conclusion can you draw about the slope coefficient?

(f) Test the hypothesis H0: 0 0 versus H1: 0 0 using 0.05. What conclusions can you draw about the best model?

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Dollars kWh Dollars kWh 4.70 2.59 4.01 2.65 4.00 2.61 4.31 2.64 4.59 2.66 4.51 2.38 4.70 2.58 4.46 2.41 4.65 2.32 4.55 2.35 4.19 2.31 4.14 2.55 4.69 2.52 4.25 2.34 3.95 2.32