Remember - show your work! Some of the answers are on the last page - what we want to see is all your work. Otherwise you may find things written in the "Needs Corrections" Box. @ 1. Plot the given data on the graph below and answer the following questions. Advertising Budget Spent lin $5.50 $5.70 $5.80 $5.85 $6.00 | $6.05 $6.10 $6.15 $6.20 | $6.25 $6.30 $6.45 Dollars) Sales $106 $110 $113 $111 $112 $115 $113 $116 $114 $115 $113 $115 (in Dollars) a) Perform a linear regression on the data and graph the line of best fit on the graph. b) Determine the equation for the line of best fit (Round Sales (in Dollars) m and b to two decimal places) 107 c) What does the slope of the line of best fit mean in this 106 situation? T// 5.50 5 60 Advertising Budget (in Dollars) d) From the graph, approximate the value of sales from an advertising budget of $5.60.2. A typical newborn baby sleeps about 16 hours a day, whereas a typical one-year old sleeps about 13 hours a day. The table below illustrates the number of hours, n, slept in a day by 10 infants of age o, in months. Hours of a) Perform a linear regression on the data. Write the equation of Age of Infant, a, Sleep, n, (in months) the line of best fit to the nearest hundredth for both m and b. (in hours) 0.3 15.9 0.6 15.1 1.3 14.8 b) Using the regression equation found in a), predict how many 3.1 14.5 hours an infant that is 6.5 months old would sleep. 5.9 14.3 7.0 14.1 8.1 13.8 3.8 12.5 c) Is what you did in part b) an example of interpolation or 10.5 12.7 extrapolation? 11.9 12.1 d) Assuming this linear trend continues, predict how long an 18-month old infant would sleep. e) Is what you did in part b) an example of interpolation or extrapolation? f) What does the y-intercept of the line of best fit represent? 3. Indicate whether each of the following statements is True or False by writing T or F. A positive m value in the regression equation indicates the line of best fit will rise to the right. A value of R" = 0.1 indicates a strong Coefficient of Determination. A negative value of m in the regression equation and Ro = 0.4 indicates the line of best fit will fall to the right and have a weak Coefficient of Determination. R' =2 is a possible Coefficient of Determination and indicates a very strong relation between the data in the data set. When m and b are both positive in a regression equation, the slope of the line of best fit rises to the right and the y-intercept is above the x-axis on the graph.4. The graph of a polynomial function is shown below. ) How many vertices does it have? b) How would you describe the end behavior of the graph? c) What is the minimum degree of the polynomial? d) What are some other possible degrees of the polynomial? 5. The following data Is that of either a polynomial or sinusoldal relation. -2 -1 1 2 3 4 12 -211 a) Perform a regression on the data and fill in the blanks below: Polynomial Regression: R-=_ Sinusoidal Regression: R- =_ b) What is the regression equation of the model that best fits the data? (Round parameters to 3 decimal places) c) Using your regression equation or graph, what is the value of y when the value of x is equal to 2.5? 6. Use the data below to answer the questions that follow. -2.5 0 2.5 3 3.5 99.56 30.87 -3.52 -5.25 132.93 256.62 441.04 a) Do a polynomial regression of Degree 2. Record both the Coefficient of Correlation and the regression equation, with all parameters rounded to 3 decimal places. b) Do a polynomial regression of Degree 4. Record both the Coefficient of Correlation and the regression equation, with all parameters rounded to 3 decimal places. -) Which of the two above regressions is the best fit for the data, and why?7. The following data sets are sinusoidal. a) Using patterns, determine both missing values in the table. X 0 4 8 12 16 20 24 28 y -4 5 5 -4 5 -4 b) Using regression, determine the missing value in the table. time 0 1.5 3 4.5 6 6.5 height 25 50 25 25 8. The table below shows data for five recently discovered fossils. % Carbon-14 79 68 38 27 Remaining (x) Age in years (y) 425 1,950 3,191 8,000 |10,824 a) Create a scatterplot to confirm that a logarithmic function is an appropriate model for this data. b) Perform a natural logarithmic 18000 regression on the data and record the equation with the parameters rounded to integers values. (no decimals) 4-4090 c) A bone fragment indicated that 10003 it has 20.3% of Carbon-14 left in it. What is the approx. age of the bone fragment? d) If a skeleton of a mammoth is about 10,000 years old, what percentage, to the nearest whole number, of carbon-14 should be remaining?REGRESSION ANALYSIS - REVIEW ASSIGNMENT 9. Match the following graphs to their type. Sinusoidal Linear Exponential Logarithmic Polynomial