A power company wants to study the impact of air conditioners on electricity usa

Question

A power company wants to study the impact of air conditioners on electricity usage during the summer in Salt Lake City. Let x be day time high temperatures in degrees Fahrenheit. Let Y be the daily total power use of a small neighborhood in kWh. Over the summer the following data are collected on 6 different days: i:1,2,3,4,5,6 xi: 85, 90, 100, 80, 95, 90 yi: 350, 400, 500, 350, 400, 400, (a) Find the equation of the fitted regression line. (b) Estimate the power usage of the neighborhood for a 110 Fahrenheit day.

Explanation / Answer

) Find the equation of the tted regression line. The equation for the slope and intercept estimates are b = Pn i=1 (xi x)(yi y) Pn i=1 (xi x) 2 = Sxy Sxx a = y bx Therefore, we start by computing x and y: x = 1 6 (85 + 90 + 100 + 80 + 95 + 90) = 90 y = 1 6 (350 + 400 + 500 + 350 + 400 + 400) = 400 Now we can compute Sxx and Sxy: Sxx = X6 i=1 (xi 90) 2 = 25 + 0 + 100 + 100 + 25 + 0 = 250 Sxy = X6 i=1 (xi 90)(yi 400) = 5 50 + 0 0 + 10 100 + 10 50 + 0 0 = 250 + 0 + 1000 + 500 + 0 + 0 = 1750 So b = Sxy=Sxx = 1750=250 = 7 and a = y bx = 400 7 90 = 230. The equation for the tted regression line is ^y = 230 + 7x. (b) Estimate the power usage of the neighborhood for a 110 o Fahrenheit day. We simply plug in x = 110 to the equation found in the previous part. So ^y = 230 + 7 110 = 540kW h. 3. A company manufacturing pacemakers is testi

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