"9. Stock Price The equation used to predict the stock price (in dollars) at the end of the year for a restaurant chain is y=- 86+7.46x_1 - 1.61x_2
where x_1 is the total revenue (in billions of dollars) and x_2 is the shareholders' equity (in
billions of dollars). Use the multiple regression equation to predict the y-values for the
values of the independent variables.
a. x_1 = 27.6, x_2 = 15.3
b. x_1 = 24.1, x_2 = 14.6
c. x_1 = 23.5, x_2 = 13.4
d. x_1 = 22.8, x_2 =15.3"

검증된 단계별 안내

Identify the multiple regression equation given:

y = - 86 + 7.46 - 1.61

, where

x_1

is total revenue and

x_2

is shareholders' equity.

For each set of values of

x_1

and

x_2

, substitute the numbers into the regression equation. For example, for part (a), substitute

x_1 = 27.6

and

x_2 = 15.3

Calculate the product of the coefficient and the corresponding independent variable for each term: multiply 7.46 by

x_1

and multiply -1.61 by

x_2

Add the constant term (-86) to the sum of the two products calculated in the previous step to find the predicted stock price

y

Repeat steps 2 to 4 for each set of values (b, c, and d) to find the predicted stock prices for all given independent variable values.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Multiple Linear Regression

Multiple linear regression models the relationship between one dependent variable and two or more independent variables by fitting a linear equation. It estimates how changes in each independent variable affect the dependent variable, holding others constant. This method helps predict outcomes based on several predictors simultaneously.

Interpreting Regression Coefficients

Regression coefficients represent the expected change in the dependent variable for a one-unit increase in an independent variable, assuming other variables remain constant. For example, a coefficient of 7.46 for x₁ means the stock price increases by $7.46 billion for each additional billion in revenue, all else equal.

Using the Regression Equation for Prediction

To predict the dependent variable, substitute given values of independent variables into the regression equation and calculate the result. This process provides estimated outcomes, such as predicted stock prices, based on specific input values for revenue and shareholders' equity.