Data from New York City was collected for various years, measuring X = the cost of a slice of cheese pizza and Y = the cost of a subway ticket. A model was found: 𝑦̂ =0.0329+0.969𝑥y^=0.0329+0.969x with 𝑟=0.87r=0.87. Which of the following is correct?
Added by Lindsay H.
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The equation \( \hat{y} = 0.0329 + 0.969x \) represents a linear regression model where \( \hat{y} \) is the predicted cost of a subway ticket (Y) based on the cost of a slice of cheese pizza (X). The coefficient \( 0.969 \) indicates that for every one unit Show more…
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Use the same data sets as Exercises 13-28 in Section 10-1. In each case, 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 on page 484. Use the pizza costs and subway fares to find the best predicted subway fare, given that the cost of a slice of pizza is $\$ 3.00$. Is the best predicted subway fare likely to be implemented? $$ \begin{array}{l|c|c|c|c|c|c|c|c|c} \hline \text { Year } & 1960 & 1973 & 1986 & 1995 & 2002 & 2003 & 2009 & 2013 & 2015 \\ \hline \text { Pizza Cost } & 0.15 & 0.35 & 1.00 & 1.25 & 1.75 & 2.00 & 2.25 & 2.30 & 2.75 \\ \hline \text { Subway Fare } & 0.15 & 0.35 & 1.00 & 1.35 & 1.50 & 2.00 & 2.25 & 2.50 & 2.75 \\ \hline \text { CPI } & 30.2 & 48.3 & 112.3 & 162.2 & 191.9 & 197.8 & 214.5 & 233.0 & 237.2 \\ \hline \end{array} $$
Correlation And Regression
Regression
Year 1960 1973 1986 1995 2002 2003 Cost of slice of Pizza 0.15 0.35 1.00 1.25 1.75 2.00 Subway fare 0.15 0.35 1.00 1.35 1.50 2.00 CPI 30.2 48.3 112.3 162.2 191.9 197.8 Using the data in the table, construct a scatter plot of the pizza cost (x) versus the subway fare (y). Determine the regression line including the correlation coefficient (r) and the explained variation (r2). Show your scatter plot and line on a graph. Explain what the y-intercept, slope, r and r2 mean and whether the relationship makes any sense. (Explain how you you got answers)
Adi S.
Use the value of the linear correlation coefficient $r$ to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. $r=0.992$ ( $x=$ cost of a slice of pizza, $y=$ subway fare in New York City)
Correlation and Regression
Prediction Intervals and Variation
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