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.) r² =_______________ % C. Based on the data, calculate the regression line (each value to three decimal places) y =___________ x + _______________

Run a regression analysis on the following bivariate set of data with y as the response variable. X y 9.8 75.6 17.1 50.7 62 71.6 41.4 60.4 44.8 37.7 52.6 40.6 60.1 10.4 55.6 38.9 74.2 -6.6 49.7 33.6 43.9 54.8 Verify that the correlation is significant at an a = 0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 45.9 on the response variable. What is the predicted explanatory value? X =

Run a regression analysis on the following bivariate set of data with y as the response variable. 58.6 53.6 20 43 24.6 44.1 9.7 40.8 55.1 57.4 -10.3 33.1 39.1 44.9 27.8 48.4 2 33.8 37.6 51.2 52.5 54.3 -12.6 35 Find the correlation coefficient and report it accurate to three decimal places. 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.) 9% Based on the data, calculate the regression line (each value to three decimal places) y = x+ Predict what value (on average) for the response variable will be obtained from a value of 53 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 =

Run a regression analysis on the following bivariate set of data with y as the response variable. x y 59.6 57.3 20.1 61.9 8 87.2 0.1 91.7 31.7 67.6 31.9 62 19.9 74.7 33.1 85.4 0.8 82.8 56.3 59.4 3.7 90.7 Verify that the correlation is significant at an α=0.05α=0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 89.2 on the response variable.What is the predicted explanatory value?x =

Run a regression analysis on the following bivariate set of data with y as the response variable. x y 60.5 38.5 81.4 13.6 3.5 132.1 52.8 69.8 51.1 30 81.1 11.4 47.1 50 23 119.2 57.9 45.2 58.6 31.8 55.9 98.5 47.6 52 Verify that the correlation is significant at an α=0.05.If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 126.3 on the response variable.What is the predicted explanatory value? x=

Consider the following data set, where yy is the final grade in a math class and xx is the average number of hours the student spent working on math each week. hours/weekx Gradey 5 58 8 63.2 8 73.2 9 68.6 9 70.6 11 68.4 13 81.2 14 86.6 17 100 20 100 The regression equation is y=3.04⋅x+42.33y=3.04⋅x+42.33.Explain what the value of the slope means in this situation, where yy is the final grade in a math class and xx is the average number of hours the student spent working on math each week.Explain what the value of the y-intercept means in this situation.What is the predicted value for the final grade when a student spends an average of 15 hours each week on math?Grade =  Round to 1 decimal place.

The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows. The estimated regression equation for these data is ŷ=27.654+0.29x.   Brand Price Score Bose 180 76 Scullcandy 160 73 Koss 85 64 Phillips/O'Neill 70 57 Denon 80 50 JVC 45 26   a. Does the t test indicate a significant relationship between price and the overall score? Compute the value of the t test statistic. Use α=0.05 b.  Show the ANOVA table for these data. Round your answers to three decimal places (and p-value to 4 decimal places), if necessary. Do not round intermediate calculations.

A researcher intends to conduct a multiple regression on the following data set where YY is the dependent variable. X1X1 X2X2 YY 41.1 46.8 40.8 43.5 37 46.3 42.9 71.2 69.3 25.3 75 47.8 38.6 59.7 41.3 46.5 53.2 52.7 49.3 42.6 50.3 47.6 29 34.1 37.1 43.1 39.7 50.1 43.5 56.1 Calculate the following correlations and semipartial correlations with the dependent variable. Report all answers accurate to at least 3 decimal places.The correlation between x1 and y = The correlation between x2 and y =