Statistics and Probability

Run a regression analysis on the following bivariate set of data with y as the response variable. X 30.8 29.3 38.3 16.1 39.2 71.8 27.6 37.1 36.9 76.7 40.4 57. 44.4 78.9 44.2 91. 37.9 55.5 32.8 93.7 Find the correlation coefficient and report it accurate to three decimal places. r= What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.) 12 = Based on the data, calculate the regression line (each value to three decimal places) y= Predict what value (on average) for the response variable will be obtained from a value of 31.8 as the explanatory variable. Use a significance level of a = 0.05 to assess the strength of the linear correlation. What is the predicted response value? (Report answer accurate to one decimal place.) y = Landon is investigating how long his phone's battery lasts (in hours) for various brightness levels (on N a scale of 0-100). His data is displayed in the table and graph below. Brightness Level (x) 31 34 52 63 71 75 85 96 Hours (y) 7.2 5.6 5.9 3.7 3.9 1.7 3.3 1.8 10- Hours 10 20 30 40 50 60 70 80 90 100 Brightness Level a) Find the equation for the line of best fit. Keep at least 4 decimals for each parameter in the equation. b) Interpret the slope in context. O Landon should expect -0.0761 hours per brightness level. O Landon should expect -0.0761 brightness level per hour. c) What does the equation predict for the number of hours the phone will last at a brightness level of 52? hours