Fitting a straight line to a set of data yields the following prediction line: y = 5 + 2x a) Interpret the meaning of 2 b) Interpret the meaning of 5 c) Predict the value of y for x=4 d) Predict the value of y for x=0

This is a business application for this formula: A real estate agent needs to examine the relationship between the selling price of a home (y) and its square footage (x). After studying the correlation, a formula is developed to estimate the selling price that should be advertised for a home based on its square footage. The formula for this estimation (in $1,000s) is y = 98.25 + 0.11x 5. Calculate the selling price of the home if the square footage is 1,400. Selling price = _____ 6. Calculate the selling price of the home if the square footage is 2,350. Selling price = _____

From the example above, the real estate agent can predict what the advertised selling price should be. However, we realize that the selling price depends upon more than just how big the house is. The selling price also depends upon size of the yard, number of bathrooms, year the house was built, the condition of the home, the public school district, and many more variables. So, the real estate agent needs to develop a formula for multiple analyses. This is an example: y = bo + b1x1 + b2x2 + b3x3 Now we have multiple independent variables: x1 is square footage, x2 is size of yard, x3 is year house was built. We could continue on with many more independent variables to help the real estate agent accurately estimate the advertised selling price.

To practice the multiple regression, try these equations: 7. y = -80 + 0.26x1 47.2x2 x1 = 1,200 x2 = -4 y = _________ 8. y = 152 + 0.129x1 + 2.7x2 x1 = 2,000 x2 = -30 y = _________ 9. A manager at a ski resort in Vermont wanted to determine the effect that weather had on its sales of lift tickets. The manager of the resort collected data over the last two decades on the number of lift tickets sold during the last week in December (y), the total snowfall in inches (X1) and the average temperature in degrees Fahrenheit (x2). Results: Intercept = 8,308 Snowfall Coefficient = 75.59 Temperature Coefficient = -8.25 a) Write the equation. b) What is the estimate for the number of lift tickets sold during that week, if the total snowfall was 20 inches and the average temperature was 30 degrees Fahrenheit?