"1. Net Sales The equation used to predict the net sales (in millions of dollars) for a fiscal
year for a clothing retailer is y=23,769 + 9.18x_1 - 8.41x_2
where x_1 is the number of stores open at the end of the fiscal year and x_2 is the average
square footage per store. Use the multiple regression equation to predict the y-values for
the values of the independent variables.
a. x_1 = 1057, x_2 = 3698
b. x_1 = 1012, x_2 = 3659
c. x_1 = 952, x_2 = 3601
d. x_1 = 914, x_2 = 3594"

검증된 단계별 안내

Identify the multiple regression equation given:

y = 23769 + 9.18 x_1 - 8.41 x_2

, where

x_1

is the number of stores and

x_2

is the average square footage per store.

For each set of values of

x_1

and

x_2

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

x_1 = 1057

and

x_2 = 3698

Perform the multiplication for each term involving the independent variables: multiply 9.18 by

x_1

and multiply -8.41 by

x_2

Add the constant term 23769 to the results of the multiplications to calculate the predicted net sales

y

for each case.

Repeat steps 2 to 4 for each set of values given in parts (b), (c), and (d) to find all predicted net sales values.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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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. It estimates how changes in each independent variable affect the dependent variable, holding others constant. The equation y = b0 + b1x1 + b2x2 represents this, where coefficients quantify the impact of each predictor.

Interpreting Regression Coefficients

Regression coefficients indicate the expected change in the dependent variable for a one-unit increase in an independent variable, assuming other variables remain fixed. For example, a coefficient of 9.18 for x1 means net sales increase by 9.18 million dollars per additional store, all else equal.

Prediction Using Regression Equations

Prediction involves substituting given values of independent variables into the regression equation to calculate the estimated dependent variable. This process helps forecast outcomes, such as net sales, based on specific inputs like number of stores and average store size.