Exam 3 - Data and Regression Graphs!

Your Name Here

There are only two problems on this exam, both of which have multiple parts. Please feel free to ask questions during the exam.
Remember Alt+7 gives you a text cell where you can type in sentences of explanation etc...

Problem 1

The weekly U.S. regular conventional retail gas price since August 31st is given in the following table.  The first column is the actual date, the second column is the number of days past August 31st for each of the dates in column 1, the the third column is the average price of regular gas for the week starting on the date given in column 1.  Use this data to answer the following questions. 

({{Day of Year, Day Past Aug 31st, Average Price of Regular Gas}, {Aud 31, 0, $2.135}, {Sep 07, 7, $2.122}, {Sep 14, 14, $2.091}, {Sep 21, 21, $2.078}, {Sep 28, 28, $2.088}, {Oct 5, 35, $2.091}, {Oct 12, 42, $2.084}, {Oct 19, 49, $2.064}, {Oct 26, 56, $2.053}, {Nov 2, 63, $2.021}, {Nov 9, 70, $2.004}})

(a) Compute the equation of the line through the first two data points given in the variable GasData below.

GasData = {{0,2.135},{7,2.122},{14,2.091},{21,2.078},{28,2.088},{35,2.091},{42,2.084},{49,2.064},{56,2.053},{63,2.012},{70,2.004}}

(b) What does the slope of the line you computed in part (a) represent?  Relate your answer to the units on the slope.

type your answer here

(c) Plot the data given in the variable GasData.

(d) Find the equation of the regression line P(t) through the points given in GasData.

(e) Plot the regression line P(t) on the same graph with the data from GasData.

(f) Using the regression function P(t), what would you expect the price of gas to be on November 23rd?

type your answer here after you enter command(s) below

(g) On what day of the year was the gas price exactly $2.00?

type your answer here after you enter command(s) below

Problem 2

I am sure we are all tired of talking about COVID-19, but hey, that’s not going to stop us from doing a math problem related to it!  We are going to examine the cumulative number of positive COVID cases in Bryan County.  The following table is the cumulative cases in Bryan County since November 1st.  The data from this table is stored int he variable CovidData below.

({{Day (November), Positive COVID Cases in Bryan County}, {1, 1655}, {2, 1684}, {3, 1743}, {4, 1773}, {5, 1801}, {6, 1837}, {7, no data available}, {8, 1971}, {9, 1981}, {10, 2018}, {11, 2092}, {12, 2167}, {13, 2191}, {14, 2262}})

(a) Plot the data using the ListPlot command, be sure to pick an appropriate window.

CovidData={{1,1655},{2,1684},{3,1743},{4,1773},{5,1801},{6,1837},{8,1971},{9,1981},{10,2018},{11,2092},{12,2167},{13,2191},{14,2262}};

(b)  Find the equation of the regression line P(t) = m*t+b through the points given in CovidData.

(c)  Find the equation of the regression quadratic Q(t) = a*(t^2)+b*t+c through the points given in CovidData.

(d) Plot the regression line P(t) and regression quadratic Q(t) on the same graph with the data from CovidData.

(e) Use both the linear and quadratic models to yield two separate predictions of the number of cumulative cases in Bryan County by November 30th.

type your answer here after you enter command(s) below

(f) If you had a choice as to which model was the ACTUAL model for the grown of Covid cases in Bryan County, which would you hope would be the model -- linear or quadratic, and why?

type your answer here