Problem 1: Determine the MSE based on the given data. (3 points)

Time (t)	Actual Demand A(t)	Demand Forecast F(t)
1	100	100
2	80	90
3	110	100
4	100	110
5		120

MSE =

Problem 2: (6 points)

The following data were collected during a study of consumer buying patterns:

Obs.	Advertising	Actual Sales
1	$ 20,000	$ 184,400
2	$ 30,000	$ 244,000
3	$ 40,000	$ 314,200
4	$ 50,000	$ 382,200
5	$ 60,000	$ 450,200
6	$ 70,000	$ 505,300

1. Obtain a regression line for the data (2 points)
2. What % of the variation is explained by the regression line? (1 point)
3. Use the equation determined in part (b) to predict the forecasted sales based on spending $ 85,000 in advertising. (3 points)

Problem #3 (6 points)

Creative Confectioners is planning to introduce a new brownie. A small-scale taste test was conducted to assess consumers preferences (Y) concerning moisture content (X1) and sweetness (X2).

Moisture	Sweetness	Preference
2.5	4.0	69
3.0	4.5	73
3.5	5.0	72
4.0	5.5	75
4.5	6.0	74
5.0	6.5	78
5.5	7.0	80

Calculate to 3 decimal places:

1. Estimate the regression function ( Y = a + b X1 + c X2) (3 points)
2. Using the estimated regression in part (a) to predict the expected value of Y for moisture content of 6.5 and a sweetness rating of 7. (3 points)