The data shown below for the dependent variable, y, and the independent variable, x, have been collected using simple random sampling. X y 29.4 4.1 14.5 25.3 9.5 20.5 10.2 12 -3.4 27.7 13.6 1.6 19.5 11.8 21.8 23.7 a. Develop a simple linear regression equation for these data. b. Determine the predicted y value when x = 11. c. Estimate the change in the y variable resulting from the increase in the x variable of 10 units. d. Conduct a hypothesis test to determine if an increase of 1 unit in the x variable will result in the decrease of the average value of the y variable. Use a significance of 0.025.

A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N = 15 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level a = 0.01. X1 X2 Y 38.4 58.8 48.2 63.4 47.9 55.6 48.4 54.6 33.1 54.9 48.7 47.4 54.8 54.2 51.7 44.1 78.6 64.8 55.3 48 38.6 56.8 54.3 34.1 56.5 61 42.6 52.1 49.2 35.8 57.5 49.4 51.2 55.3 66.7 56.7 57.5 53.5 25.6 71.8 64.4 63.3 29.1 62.8 56.7 Sreg SS.res R F P-value =

Consider the following data set, where y is the final grade in a math class and is the average number of hours the student spent working on math each week. hours/week X 6.5 10 11 12.5 13 14.5 15 17.5 19.5 20 Grade y 66.1 63 71.4 72.5 79.2 94.3 95 91.5 100 98 The regression equation is y = 3x + 41.3. a) Explain what the value of the slope means in this situation, where y is the final grade in a math class and is the average number of hours the student spent working on math each week. O For each additional hour per week that a student studies on average, their final grade will be about 3 points. O For each additional hour per week that a student studies on average, their final grade will be about 41.3 points higher. For each additional hour per week that a student studies on average, their final grade will be about 3 points higher. O For each additional hour per week that a student studies on average, their final grade will be about 41.3 points. b) Explain what the value of the…

Which of the following is an assumption of the regression model? Select one: a. X and Y are independent variables. b. The errors of prediction are uniformly distributed. c. The error terms of X are dependent on the error terms of Y. d. There exists a linear association between variables X and Y.