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True or false If false, explain briefly. a. We choose the linear model that passes through the most data points on the scatterplot. b. The residuals are the observed \(y\) -values minus the \(y\) values predicted by the linear model. c. Least squares means that the square of the largest residual is as small as it could possibly be.

True or false II If false, explain briefly. a. Some of the residuals from a least squares linear model will be positive and some will be negative. b. Least squares means that some of the squares of the residuals are minimized. c. We write \(\hat{y}\) to denote the predicted values and \(y\) to denote the observed values.

Sophomore slump? A CEO complains that the winners of his "rookie junior executive of the year" award often turn out to have less impressive performance the following year. He wonders whether the award actually encourages them to slack off. Can you offer a better explanation?

Bookstore sales once more Here are the residuals for a regression of Sales on Number of Sales People Working for the bookstore of Exercise 5 ?: a. What are the units of the residuals? b. Which residual contributes the most to the sum that was minimized according to the least squares criterion to find this regression? c. Which residual contributes least to that sum?

Cereals For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in servings of 77 breakfast cereals produced the regression model Potassium \(=38+27\) Fiber. If your cereal provides 9 grams of fiber per serving, how much potassium does the model estimate you will get?

Engine size In Chapter 6 ?, Exercise 41 ? we examined We can examine the relationship between the fuel economy (CombinedMPG) and Displacement (in liters) for 1211 models of cars. (Data in Fuel economy 2016) Further analysis produces the regression model Combined \(M P G=33.46-3.23\) Displacement. If the car you are thinking of buying has a 4 -liter engine, what does this model suggest your gas mileage would be?

Another bowl In Exercise 15 ?, the regression model Potassium \(=38+27\) Fiber relates fiber (in grams) and potassium content (in milligrams) in servings of breakfast cereals. Explain what the slope means.

Another car The correlation between a car's engine size and its fuel economy (in mpg) is \(r=-0.774\). What fraction of the variability in fuel economy is accounted for by the engine size?

Real estate A random sample of records of home sales from Feb. 15 to Apr. \(30,1993,\) from the files maintained by the Albuquerque Board of Realtors gives the Price and Size (in square feet) of 117 homes. A regression to predict Price (in thousands of dollars) from Size has an \(R^{2}\) of \(71.4 \%\). The residuals plot indicated that a linear model is appropriate. a. What are the variables and units in this regression? b. What units does the slope have? c. Do vou think the slope is positive or \(n\) 2\. Fxnlain

What slope again? If you create a regression model for estimating the Height of a pine tree (in feet) based on the Circumference of its trunk (in inches), is the slope most likely to be \(0.1,1,10,\) or \(100 ?\) Explain.