2 - additional (not on Wiley) - due Thursday, Oct 6 Problem 1 (SSxx =Sxx, SSyy=Syy, SSxy=Sxy different notation ) Problem 2. The following table gives the temperatures(X) (in degrees Fahrenheit) at 6 P.M. and the attendance (Y) (rounded to hundreds) at a minor league baseball team's night games on 7 randomly selected evenings in May. Temperature 61 70 50 65 48 75 53 Attendance 10 16 12 15 8 20 18 a. Do you think temperature depends on attendance or attendance depends on temperature? b. Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between the two variables? c Find the least squares regression line. d. Give a brief interpretation of the values of the y-intercept and slope calculated in part c e Compute r and R2, and explain what they mean. Problem 3. Consider two hospitals A and B that have the data relating to patient condition before admission and survival outcomes after being admitted for treatment Outcome Died Survived Condition Good Bad Good Bad Hospital A Hospital B 5 295 1000 2000 10 40 800 200 (a) Compare the two hospitals' overall percentage of deaths. If you needed surgery, would you prefer Hospital A or Hospital B? (b) If you needed surgery and your condition was rated as good, which hospital would you prefer? (c) If you needed surgery and your condition was rated as bad, which hospital would you prefer? (d) Do your answers from (b) and (c) contradict your answer in (a)? What is this phenomenon called? Which hospital do you ultimately decide to be better? Problem 4 Use all three methods : Graphs , Chi-square test , Compare conditional distributions - the same way we did in class. The following table gives the two way classification of 1000 people who have been married at least once. They are classified by educational level and marital status.Is there a relationship between \"educational level\" and \"ever being divorced? Hint - p-value is close to zero (show all calculations) Problem 5 True or False a) If the correlation coefficient1r= 1, then all the data points lie exactly on a straight line. b) The correlation coefficient r is a number that indicates the direction and the strength of the relationship between the dependent variable y and the independent variable x. c) If the correlation coefficient r=0, then there is no linear relationship whatsoever between the dependent variable y and the independent variable x d) The standard deviation is a measure of the linear relationship between two quantitative variables e)The best fitting line relating the dependent variable y to the independent variable x, often called the regression or least-squares line, is found by minimizing the sum of the squared differences between the data points and the line itself. f) The scatterplot is a graph that is used to graphically represent the relationship between two quantitative variables. g) If the linear relationship between the dependent and independent variables is positive, the scatterplot will show the data points on the (x, y) plane generally moving from the lower left corner to the upper right corner. h) If the correlation coefficient between the independent variable x and the dependent variable y is 0.87, then the best fitting line would have a slope equal to 0.87. i)If two variables have a correlation coefficient equal to 0.005, this means that there is no relationship between the two variables. j) A perfect correlation between two variables will always produce a correlation coefficient of + 1 Problem 6 - extra credit