The coefficient of determination, r 2, is The fraction of the variation in the value of y that is explained by the regression line and the explanatory.

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Presentation transcript:

The coefficient of determination, r 2, is The fraction of the variation in the value of y that is explained by the regression line and the explanatory variable. A recipe for r A recipe to explain the coefficient of determination (r 2) The linear association between x and y predicts __r 2 %___ of the variability in y. A recipe for slope On average, for each unit increase in x, there is an increase (or decrease) of b in y. There is a _(strength)___, ___(direction)____, linear relationship between __(explanatory)__ and __(response)__.

b. Does there appear to be an association between the odometer reading and the trade-in value? If so, what is it? c. Use your calculator to determine the least-squares regression line (LSRL). Trade in value depends on odometer reading d. Provide an interpretation of the slope of this line in the context of these data. On average, for each 1000 mile increase in odometer reading there is a decrease of $26.68 in trade in value. f. Find the correlation coefficient for the relationship. Interpret this number. r = There is a strong, negative linear relationship between the odometer reading and the trade in value.

h. Predict the trade-in value of a car with 60,000 miles. g. Find the coefficient of determination for the relationship. Interpret this number. r 2 =.7982 The linear association between the odometer reading and the trade in value predicts 79.82% of the variability in the trade in value. The predicted trade in value for a car with an odometer reading of 60, 000 miles is $4, 019.