DATA: A random sample of 15 states and their average 2018 SAT scores and SAT participation rates is given below. If you are native to the east coast you may not know that many state universities either prefer the ACT or have their own state college tests. This is particularly true in the midwestern states. Most students will take the state test or ACT and only those students seeking to attend out of state colleges will take the SAT.

State: Mississippi Score: 1240 Participation: 2%	State: Rhode Island Score: 1060 Participation: 71%	State: Texas Score: 1020 Participation: 62%	State: Wyoming Score: 1230 Participation: 3%	State: South Dakota Score: 1220 Participation: 3%
State: Maine Score: 1010 Participation: 95%	State: Virginia Score: 1100 Participation: 65%	State: New York Score: 1050 Participation: 67%	State: New Hampshire Score: 1050 Participation: 90%	State: New Mexico Score: 1140 Participation: 11%
State: Vermont Score: 1110 Participation: 60%	State: Florida Score: 1020 Participation: 83%	State: Pennsylvania Score:1070 Participation: 65%	State: Oklahoma Score: 1050 Participation: 7%	State: Kansas Score: 1260 Participation: 4%

1. Construct a scatter plot for ordered pairs (x is participation rate, y is average SAT score). Please graph this on your computer and attach to the quiz. Remember to label each axis. Do not bunch your data into a small section of the graph, remove unnecessary parts of the scale. Comment on the relationship of this data: if participation rate goes up, then ______________________________________. (6 pts)

After you have created your scatter plot, answer the following:

(a) Determine the correlation coefficient r. Use technology and round to 4 decimal places. Explain what the correlation coefficient measures. (2 pts)

(b) Determine the equation for the line of best fit . Use technology and round a, b to 2 decimal places. You may include this line and its equation on your scatter plot but please also write the equation here. (2 pts)

(c) Determine the coefficient of determination r² (round to 4 decimal places). Explain what the coefficient of determination measures. (2 pts)

(d) Calculate the mean of the state SAT scores (to one decimal place) (2 pts)

(e) Is the correlation coefficient statistically significant? Show your calculations and answer yes or no.

(2 pts)

(f) What does it mean to be statistically significant? Explain. (2 pts)

(g) Suppose a state has a 15% participation rate of students taking the SAT. What is the best predicted state SAT score? That is, will you be using the mean of the state SAT scores as your best guess or will you use your regression equation to predict the state SAT score? Calculate and Explain your answer. (4 pts)

(h) Create a residual plot for this data. The residual plot will be the ordered pairs (x, y - ). Please graph this on your computer and attach to the quiz. Does the residual plot suggest that a linear model is a good fit for the data? Explain your answer. (6 pts)