A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=a+bx a=36.039 b=-1.213 r2=0.403225 r=-0.635 Suppose that you run a correlation and find the correlation coefficient is 0.604 and the regression equation is y = 0.8 + 5.3 x . The mean for the x data values was 4, and the mean for the y data values was 20.6. A T Test for the slope of the regression line is performed, and the p-value is greater than the level of significance of 0.05. Use the appropriate method to predict the y value when x is 1.8. Assume the correlation is significant (p-value < ), and use this to predict the number of situps a person who watches 10.5 hours of TV can do (to one decimal place) Run a regression analysis on the following bivariate set of data with y as the response variable. x y 100.6 135.3 116.2 110.3 78.1 47.3 58 12.3 88.8 127.1 65.3 11.1 66.5 36.3 57.8 20.5 79.3 45.2 78 60.8 63.3 31 94.2 93.5 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.) r = % Based on the data, calculate the regression line (each value correct to 1 decimal place) y = + x Predict what value (on average) for the response variable will be obtained from a value of 92.6 as the explanatory variable. Use a significance level of = 0.05 to assess the strength of the linear correlation. What is the predicted response value? (Report answer accurate to one decimal place.) y = Randall is investigating how long his phone's battery lasts (in hours) for various brightness levels (on a scale of 0-100). His data is displayed in the table and graph below. Brightness Level (x) 16 31 45 47 49 56 61 86 Hours (y) 6.3 5.9 5.2 5.4 4.4 4.6 3.2 4 10 20 30 40 50 60 70 80 90 100 110 1 2 3 4 5 6 7 8 9 -1 Brightness Level Hours 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. Randall should predict an increase of 0.0408 hours per brightness level. Randall should predict a decrease of 0.0408 hours per brightness level. c) What does the equation predict for the number of hours the phone will last at a brightness level of 86? hours d) What is the residual for the point (86,4)? hours In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation as y = 13 + 0.85 x where y is the final-exam score and x is the score on the first test. Demetrius scored 70 on the first test. What is the predicted value of the Demetrius's score on the final exam? Demetrius scored 66.5 on the final exam. What is the value of the residual