# Question: A regression formula that gives a parabolic shape instead of

A regression formula that gives a parabolic shape instead of a straight line for the relationship between two variables is μy = α + β1x + β2 x2.

a. Explain why this is a multiple regression model, with x playing the role of x1 and x2 (the square of x) playing the role of x2.

b. For x between 0 and 5, sketch the prediction equation (i) = 10 + 2x + 0.5x2 and (ii) = 10 + 2x - 0.5x2.This shows how the parabola is bowl-shaped or mound-shaped, depending on whether the coefficient x2 is positive or negative.

a. Explain why this is a multiple regression model, with x playing the role of x1 and x2 (the square of x) playing the role of x2.

b. For x between 0 and 5, sketch the prediction equation (i) = 10 + 2x + 0.5x2 and (ii) = 10 + 2x - 0.5x2.This shows how the parabola is bowl-shaped or mound-shaped, depending on whether the coefficient x2 is positive or negative.

## Answer to relevant Questions

At the x value where the probability of success is some value p , the line drawn tangent to the logistic regression curve has slope βp(1 - p). a. Explain why the slope is β / 4 when p = 0.5. b. Show that the slope is ...For the House Selling Prices OR data file on the text CD, the output shows the result of conducting an ANOVA comparing mean house selling prices (in $1000) by Age Category ( New = 0 to 24 years old, Medium = 25 to 50 years ...Refer to the previous exercise. a. Set up indicator variables to represent the three service centers. b. The prediction equation is = 7.1 + 0.5x1 + 0.7x2. Show how the terms in this equation relate to the sample means of ...In Example 10, the coefficient of the manure-level indicator variable m is 1.96. a. Explain why this coefficient is the estimated difference in mean corn yield between the high and low levels of manure, for each level of ...Refer to the previous exercise. a. Set up indicator variables for protein source and for protein level, and specify a regression model with the effects both of protein level and protein source on weight gain. b. Fit the ...Post your question