Crossroad Inn is a small bed-and-breakfast inn. Following table shows the weekly

Question

Crossroad Inn is a small bed-and-breakfast inn. Following table shows the weekly bar sales and number of guests registered for the same week. The manager assumes the bar sales are related to the number of registered guests. Week Guests Bar Sales 1 50 $2,550 2 45 $2,475 3 33 $2,295 4 40 $2,400 5 60 $2,700 6 30 $2,250 7 52 $2,580 a)       Develop a simple linear regression model that relates bar sales to guests (not to time). [10 points] b)      If the forecast for 8th week is 55 guests, how much bar sales can be expected? [10 points]

Explanation / Answer

Let’s assume that the linear regression equation for bar sales forecast is represented by the following equation

y = a + b *x…………………….. (1)

Where a is the y-intercept of the line and b is the slope of the line. Formula to calculate the a and b are following

Slop b = Sum of {(x-xbar)*(y-ybar)}/ Sum of {(x-xbar)^2}

Intercept a = ybar - b * x bar

Where,

x is the number of guests and y is the bar sales

Now putting the value of a & b in equation (1), we get

Y = 1800 + 15 * x

If the forecast for 8th week is 55 guests, bar sales can be expected

Y = 1800 + 15 * 55 = 2625

period Guests (x) Bar Sales ($, y) x - x bar y - y bar (x-xbar)*(y-ybar) (x-xbar)^2 (y-ybar)^2 1 50 2550 7 105.00 735.00 49.0 11025.0000 2 45 2475 2 30.00 60.00 4.0 900.0000 3 33 2295 -10 -150.00 1500.00 100.0 22500.0000 4 40 2400 -3 -45.00 135.00 9.0 2025.0000 5 60 2700 17 255.00 4335.00 289.0 65025.0000 6 30 2250 -13 -195.00 2535.00 169.0 38025.0000 52 2580 9 135.00 1215.00 81.0 18225.0000 Mean 43 2445.00 x bar ybar Sum 10515.00 701.00 157725.00 slop b = Sum of {(x-xbar)*(y-ybar)}/ Sum of {(x-xbar)^2} 15.00 Intercept a = ybar - b * x bar 1800.00 Y = a + bx If guest x=55, Y = a + b *55 2625

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