Chicken sandwiches are often advertised as a healthier alternative to beef because many are lower in fat. Tests on 11 brands of fast-food chicken sandwiches produced the following summary statistics and scatterplot from a graphing calculator: Fat: mean 20.6, standard deviation 9.8 Calories: mean 472.7, standard deviation 144.2 Correlation: 0.947 Write the equation of the regression line. Explain the meaning of the slope and the y-intercept. What does it mean if a certain sandwich has a negative residual? If a chicken sandwich and a burger each advertised 35 grams of fat, which would you expect to have more calories?  

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We are given the following information about chicken sandwiches.

Let x represent the grams of fat. Then the mean of 11 sandwiches is `bar(x)=20.6` with a standard deviation of `s_x=9.8`

Let y (the dependent variable) represent the total calories. Then the mean is `bar(y)=472.7` with a standard deviation of `s_y=144.2`

The correlation coefficient `r=0.947` indicates a strong, positive linear relationship between these variables. (In other words, as the grams of fat increase, we expect to see the calories increase also.)

(1) To calculate the regression line, we first assume that there is a linear relationship between the variables. The scatterplot should show points roughly along a "line," and the...

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