math question -you need to show your work-due day today 19.30
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MA 151 Test 2 Name: Directions: Show all work in a neat and organized fashion on your own paper. Copy your answers into the space provided on the right side of this page. Do not show work on this paper; it will neither be considered nor graded. 1. I have a data set consisting of the following three points: (1,5), (2,7), (5,15). I propose two different lines as a reasonable fit for this data: 3 1 and
2. Which line is a better fit, and why? Do not guess or base your answer on visual inspection of a graph; there is a specific procedure you must follow to answer this question. 2. In a model for optimizing revenue, I find that the profit y for a particular item, as a function of price p, is given by 25 400 1200. What is the optimal price I should charge for that product, and what is my profit if I charge that price? 3. In an exponential regression model, Excel finds a best-fit curve of 4,845 . . Convert this equation into one of the form , and give the value of y when x=3.15. 4. Given the following set of 5 points, use the technique we explored in class to decide whether the data is approximately linear, approximately exponential, or neither. If you find that the data is approximately linear, give the approximate slope; if you find that the data is approximately exponential, give the approximate base. You must show work to get any credit for this question. The data points are: (3,25), (4,33), (5,50), (6,69), (7,96). 5. Based on data we have collected from teens and adults, we determine that a person’s weight w (in pounds) can be estimated from his or her height h (in inches) by the equation 3 40. Use this formula to estimate the weight of someone who is 4’9” tall. 6. According to our formula in question 5, a slightly premature infant whose length is 12” would have a weight of -4 lbs., which of course is nonsense. Explain, based on what we’ve discussed in class, why our formula has apparently failed. Assume the formula is valid as it is described in the earlier question. 7. In a particular linear model which models a set of data points, I calculate the sum of squared error between the estimated points (from the equation of the line) and the actual data, and the sum turns out to be zero. What does that tell me about the points and the line? Extra Credit (do after the test, and turn in by 11:59 p.m. Friday, March 6): Make a copy for yourself of the three points given in question 1. Use Excel to find the best-fit line for those points, and calculate the sum of squared error for that line.
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