Regression and Predictions
Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1.

Find the regression equation, letting the first variable be the predictor (x) variable.
Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5.
Subway and the CPI Use the subway/CPI data from the preceding exercise. What is the best predicted value of the CPI when the subway fare is \$3.00?

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Identify the predictor variable (x) and the response variable (y). In this case, the subway fare is the predictor variable (x), and the Consumer Price Index (CPI) is the response variable (y).

Use the given data set to calculate the regression equation. The regression equation is typically of the form y = mx + b, where m is the slope and b is the y-intercept. To find m and b, use the formulas: m = (Σ(xy) - n(μx)(μy)) / (Σ(x²) - n(μx²)) and b = μy - m(μx), where μx and μy are the means of x and y, respectively.

Substitute the calculated values of m (slope) and b (intercept) into the regression equation to obtain the final equation.

To predict the CPI when the subway fare is \$3.00, substitute x = 3.00 into the regression equation y = mx + b. This will give the predicted value of y (CPI).

Verify the prediction by ensuring that the value of x = 3.00 lies within the range of the data set used to calculate the regression equation. If it does, the prediction is valid; otherwise, it may be an extrapolation and less reliable.

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주요 개념

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

Regression Analysis

Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. In this context, it helps to determine how changes in the predictor variable (subway fare) affect the predicted value of the response variable (CPI). The output is typically a regression equation that can be used for making predictions.

Predictor and Response Variables

In regression analysis, the predictor variable (independent variable) is the one used to predict the value of another variable, known as the response variable (dependent variable). In this case, the subway fare is the predictor variable, while the Consumer Price Index (CPI) is the response variable. Understanding the roles of these variables is crucial for interpreting the regression results.

Prediction Procedure

The prediction procedure involves using the regression equation to estimate the value of the response variable based on a specific value of the predictor variable. This typically includes substituting the predictor value into the regression equation to calculate the predicted response. In this scenario, the procedure will be applied to find the CPI when the subway fare is set at $3.00.