Determine by a matrix method the equation of the line of regression for Y on X1 and X2. Use your results in i. to predict the expected profit of the firm in a month where the average outside temperature was -2 degrees and the average number of daily customers compliment was 3.
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Variable Y represents the profit (in thousand of dollars ) of an indoor heating repairs firm in a small town , over four consecutive months. The variable X1 represents the average outside temperature for the month, and the variable X2 represents the average number of daily customer complements(positive) or complaints(negative). For a month in which X2 is positive there were more complements than complaints but for a month in which X2 is negative there were more complaints than compliments. Using the information about variables
|
Month |
X1 |
X2 |
Y |
|
NOVEMBER |
-5 |
5 |
11 |
|
DECEMBER |
-4 |
4 |
11 |
|
JANUARY |
-1 |
1 |
8 |
|
FEBRUARY |
2 |
-3 |
2 |
- Determine by a matrix method the equation of the line of regression for Y on X1 and X2.
- Use your results in i. to predict the expected profit of the firm in a month where the average outside temperature was -2 degrees and the average number of daily customers compliment was 3.
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