Let ŷ represent the profit (in thousand: of dollars) for a certain company x years after 1975. A statistician calculates a linear model ŷ = -1.54x + 32.1 Use the model to estimate the profit in 1979. Your answer should be in dollars, no thousands of dollars. Profit =$

The growth rate of the speed of sound in relation to the temperature in degrees Fahrenheit is a linear function. The speed of sound at 0 degrees Fahrenheit is 1052.3 feet per second. For every 1 degree Fahrenheit rise in temperature, the speed of sound increases by 1.1 feet per second.  A. Identify the initial value of linear function that gives the speed of sound in terms of temperature. B. A 20 degree Fahrenheit rise in temperature would provide what increase in the speed of sound? C. What would the speed of sound be after a 67 degree Fahrenheit rise in temperature?

The accompanying data represent the yearly amount of solar power installed (in megawatts) in a particular area from 2000 through 2008. The trend forecasting equations below were found, where X is the number of years after 2000. Complete parts (a) through (d) below. = -10.711 +28.9000X₁ ₁ = 22.70 +0.259X; +3.5801X? Click the icon to view the data table. a. Compute the standard error of the estimate (Syx) for each model. Linear Quadratic Syx 22.431 8.032 (Round to three decimal places as needed.) b. Compute the MAD for each model. Linear Quadratic MAD 64.222 66.873 (Round to three decimal places as needed.) c. On the basis of (a) and (b) and the principle of parsimony, which forecasting model would you select? The model with the smallest values of Syx and MAD should be used, which is the quadratic model.

Linear models can be used to predict buying habits of consumers. Suppose that a survey found that in 2008, 18% of the consumers surveyed in a group bought designer frames for their eyeglasses. In 2011, the percentage climbed to 24 % a. Assume the percentage of people buying frames is a linear function of time, and find an equation for the percentage of people buying designer frames. Let t correspond to the number of years since 2008 P(t) b. Use your equation to predict the percentage of people buying designer frames in 2014 The model predicts the percentage of people buying designer frames in 2014 will be | c. Use your equation to predict when the percentage of people who buy designer frames will reach 50 % The model predicts in the year 1, 50% of people will buy designer frames d. Do you think you can use this model to predict the percentage of people buying designer frames in the year 2051? Why or why not?