# MARYLAND MATH 107 Curve-fitting Project Linear Regression Model NEW

MARYLAND MATH 107 Curve-fitting Project  Linear Regression Model NEW

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Curve-fitting Project – Linear Regression Model

B. Background A linear regression is a technique for examining real-world data to determine if the data follows a linear model. In other words, given some data points, can we reliably use a line to model the points and make predictions? There are tools available which will find the best line that approximates a set of data points. The tools provide a measure of how well the line fits the data values. If a line exists that is a good fit, then we can use the line to make predicitions for values we do not have. There are a variety of reference materials available to help you complete the project. • Your textbook has a brief introduction to mathematical models on pages 114 – 117. • The following YouTube video is an introduction to Linear Regression. This is background/motivation rather than how to actually compute a linear regression. Introduction to Linear Regression • Suzanne Sands (a teacher at UMUC) has made two video tutorials that show you how to compute a linear regression using Excel. See: Excel Linear Regression Tutorial #1 Excel Linear Regression Tutorial #2 • Suzanne has also done a video on using a free online tool (www.meta-calculator.com) to do a linear regression. See: Online Linear Regression Tutorial
D. Suggested Topics You are welcome to use a topic of your own. Several ideas are listed below. If you are using your own topic, it is important to note that you topic cannot involve a physical law that is defined to be linear. For example, an inappropriate choice for a topic would be to relate the time it takes to travel somewhere 2 with the distance travelled. The reason this is an inappropriate choice is that physical laws tell us that distance = speed × time, which is a linear relationship. Further, since we already know the equation of the line, doing a linear regression for this case is not interesting! Another example of an inappropriate choice for a topic is data that exhibits a linear trend but have no apparent cause to do so. For example, if you graph the divorce rate in Maine vs the consumption of margarine, you will find these values correlated. This is an example of an inappropriate topic for the project because we have no reason to believe that margarine causes divorces! The goal of this project is to use data that appears to be roughly linear but where the formula or equation is not known ahead of time and show how the data can be modelled with a line found through linear regression. • Choose an Olympic sport – an event that interests you. Go to http://www.databaseolympics.com/ and collect data for winners in the event for at least 8 Olympic games (dating back to at least 1980). (Example: Winning times in Men’s 400 m dash). Make a quick plot for yourself to “eyeball” whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different event.) After you find the line of best fit, use your line to make a prediction for the next Olympics (2014 for a winter event, 2012 or 2016 for a summer event ). NOTE: Not all Olympic events lend themselves to this type of analysis. For instance, downhill skiing times from different Olympics cannot be compared because the race courses can be very different, unlike swimming events where the same swimming pool specifications are used with each Olympics. • Choose a particular type of food. (Examples: Fish sandwich at fast-food chains, cheese pizza, breakfast cereal) For at least 8 brands, look up the fat content and the associated calorie total per serving. Make a quick plot for yourself to “eyeball” whether the data exhibit a relatively linear trend. (If so, proceed. If not, try a different type of food.) After you find the line of best fit, use your line to make a prediction corresponding to a fat amount not occurring in your data set.) Alternative: Look up carbohydrate content and associated calorie total per serving. • Choose a sport that particularly interests you and find two variables that may exhibit a linear relationship. For instance, for each team for a particular season in baseball, find the total runs scored and the number of wins. Excellent websites: http://www.databasesports.com/ and http://www.baseballreference.com/

# MARYLAND MATH 107 Quiz 1 NEW

MARYLAND MATH 107 Quiz 1 NEW

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1a. (2 pts) Which of the following represents the distance between 12.4 and – 6.9 on the number line?                 Indicate your choice .

2. (3 pts) Write the interval notation corresponding to the set notation {x | x ≥ – 4}.
3. (6 pts) Consider the interval (– ∞, 0]. For each numerical value below, is it in the interval or not? (Just answer Yes or No)
4. (6 pts) Simplify . Show work. Make sure that your final answer has no negative exponents.
5. (10 pts) Simplify . Show work. Make sure that your final answer has no negative exponents.
6. (8 pts) Compute (1.40×
10^(-6))/( 9.3 × 10^5 ) . Show some work. Write the answer using scientific notation.
7. (6 pts. each) Factor. (Work not required to be shown).
8. (12 pts) Perform the indicated operations and simplify: 2 . Show work.
9. (8 pts) Solve the equation . Show work.
10. (8 pts) Solve the equation . Show work.
11. (9 pts) Simplify: . Show work
12. (8 pts) Simplify: . Show work. Give the exact answer (including a radical).
13. The Point (0, 1) is on a circle that has center (-3, 5) find the length of the diameter of the circle.