Ch. 9 - Correlation and Regression

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 9 - Correlation and Regression

문제 9.R.27

9장, 문제 9.R.27

"In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables.
27. An equation that can be used to predict fuel economy (in miles per gallon) for automobiles is
y=41.3- 0.004x_1 - 0.0049x_2
where x_1 is the engine displacement (in cubic inches) and x_2 is the vehicle weight (in
pounds).
a. x_1 = 305, x_2 = 3750
b. x_1 = 225, x_2 = 3100
c. x_1 = 105, x_2 = 2200
d. x_1 = 185, x_2 = 3000"

검증된 단계별 안내

Identify the multiple regression equation given:

y = 41.3 - 0.004 x 1 - 0.0049 x 2

, where

x 1

is engine displacement and

x 2

is vehicle weight.

For each set of values of

x 1

and

x 2

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

305

for

x 1

and

3750

for

x 2

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

0.004

x 1

and

0.0049

x 2

Subtract the results of these multiplications from the constant term

41.3

to find the predicted value of

y

(fuel economy) for each case.

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

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주요 개념

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Multiple Regression Equation

A multiple regression equation models the relationship between one dependent variable and two or more independent variables. It predicts the dependent variable by combining the independent variables, each multiplied by their respective coefficients, plus a constant term. This allows for understanding how changes in predictors affect the outcome.

Interpretation of Regression Coefficients

Regression coefficients represent the expected change in the dependent variable for a one-unit increase in an independent variable, holding other variables constant. Negative coefficients indicate an inverse relationship, meaning as the predictor increases, the predicted value decreases.

Prediction Using Regression Models

Prediction involves substituting given values of independent variables into the regression equation to calculate the estimated dependent variable. This process helps estimate outcomes based on known inputs, useful for forecasting or decision-making.