1. STAT E100 Section Week 6 – Exam Review

2. Review - Take the practice exam like you would take any test, be strict on yourself! Timing can be a big factor and, at the end, be sure to go back over the answers. - Don’t forget to go back over your homework solutions carefully. - Take advantage in-person and online office hours for questions. - Spend time organizing you cheat sheet, it will pay off during the exam!

3. PRACTICE EXAM QUESTION #1 1. Below is the histogram for the number of medals won for the n = 203 countries that participated in the 2008 Summer Olympics in Beijing, along with the detailed summary statistics for this variable: a. Is this distribution symmetric, left-skewed, or right-skewed? How do you know? b. The mean for these data is 4.70. Give a reasonable guess of the median for these data. c. Based on the rule we used in class and in your text, are there any potential low or high outliers in the dataset? Show your work.

4. PRACTICE EXAM QUESTION #1 1. Below is the histogram for the number of medals won for the n = 203 countries that participated in the 2008 Summer Olympics in Beijing, along with the detailed summary statistics for this variable: a. Is this distribution symmetric, left-skewed, or right-skewed? How do you know? The distribution is right-skewed (definitely not symmetric) b. The mean for these data is 4.70. Give a reasonable guess of the median for these data. 0, 1, 2, or 3. It should be less than or equal to 3, which is the 3rd quartile, and greater than or equal to 0, the first quartile. (It should also be a whole number). c. Based on the rule we used in class and in your text, are there any potential low or high outliers in the dataset? Show your work. IQR=3 Upper Q3+1.5*IQR = 3+4.5 = 7.5 Lower=Q1-1.5*IQR = 0-4.5 = -4.5 There are upper outliers (at least 4 of them) but no lower ones.

5. PRACTICE EXAM QUESTION #2 2. The following questions are multiple choice and DO NOT require any explanation or for you to show your work. Note: they are unrelated to each other. a. If the coefficient of determination (R2 ) is 0.975 in a simple regression, then which of the following is true regarding the slope of the regression line? a) All we can tell is that it must be positive. b) It must be 0.975 c) It must be 0.987 d) Cannot tell the sign or the value. b. Heights of college women have a distribution that can be approximated by a normal curve with a mean of 65 inches and a standard deviation equal to 3 inches. About what proportion of college women are between 65 and 67 inches tall? a) 0.75 b) 0.50 c) 0.25 d) 0.17 c. Consider the annual salaries of mutual fund managers in the Boston area. The mean salary is $450,000 and the median salary is $380,000. Circle the correct answer below. The probability that the salary of a randomly selected mutual fund manager from the Boston area is larger than the mean of $450,000 is (Circle the appropriate answer): a) ≤ 0.5 b) = 0.5 c) ≥ 0.5 d) Cannot be determined

6. PRACTICE EXAM QUESTION #2 2. The following questions are multiple choice and DO NOT require any explanation or for you to show your work. Note: they are unrelated to each other. a. If the coefficient of determination (R2 ) is 0.975 in a simple regression, then which of the following is true regarding the slope of the regression line? a) All we can tell is that it must be positive. b) It must be 0.975 c) It must be 0.987 d) Cannot tell the sign or the value. b. Heights of college women have a distribution that can be approximated by a normal curve with a mean of 65 inches and a standard deviation equal to 3 inches. About what proportion of college women are between 65 and 67 inches tall? a) 0.75 b) 0.50 c) 0.25 d) 0.17 c. Consider the annual salaries of mutual fund managers in the Boston area. The mean salary is $450,000 and the median salary is $380,000. Circle the correct answer below. The probability that the salary of a randomly selected mutual fund manager from the Boston area is larger than the mean of $450,000 is (Circle the appropriate answer): a) ≤ 0.5 b) = 0.5 c) ≥ 0.5 d) Cannot be determined

7. PRACTICE EXAM QUESTION #2 2. The following questions are multiple choice and DO NOT require any explanation or for you to show your work. Note: they are unrelated to each other. a. If the coefficient of determination (R2 ) is 0.975 in a simple regression, then which of the following is true regarding the slope of the regression line? a) All we can tell is that it must be positive. b) It must be 0.975 c) It must be 0.987 d) Cannot tell the sign or the value. b. Heights of college women have a distribution that can be approximated by a normal curve with a mean of 65 inches and a standard deviation equal to 3 inches. About what proportion of college women are between 65 and 67 inches tall? a) 0.75 b) 0.50 c) 0.25 d) 0.17 c. Consider the annual salaries of mutual fund managers in the Boston area. The mean salary is $450,000 and the median salary is $380,000. Circle the correct answer below. The probability that the salary of a randomly selected mutual fund manager from the Boston area is larger than the mean of $450,000 is (Circle the appropriate answer): a) ≤ 0.5 b) = 0.5 c) ≥ 0.5 d) Cannot be determined

8. PRACTICE EXAM QUESTION #2 2. The following questions are multiple choice and DO NOT require any explanation or for you to show your work. Note: they are unrelated to each other. a. If the coefficient of determination (R2 ) is 0.975 in a simple regression, then which of the following is true regarding the slope of the regression line? a) All we can tell is that it must be positive. b) It must be 0.975 c) It must be 0.987 d) Cannot tell the sign or the value. b. Heights of college women have a distribution that can be approximated by a normal curve with a mean of 65 inches and a standard deviation equal to 3 inches. About what proportion of college women are between 65 and 67 inches tall? a) 0.75 b) 0.50 c) 0.25 d) 0.17 c. Consider the annual salaries of mutual fund managers in the Boston area. The mean salary is $450,000 and the median salary is $380,000. Circle the correct answer below. The probability that the salary of a randomly selected mutual fund manager from the Boston area is larger than the mean of $450,000 is (Circle the appropriate answer): a) ≤ 0.5 b) = 0.5 c) ≥ 0.5 d) Cannot be determined

9. PRACTICE EXAM QUESTION #3 3. An observational study collected the monthly unemployment rate in the entire US (unemployment: in percentage points, ranging from 4.4% to 10%) along with the monthly inflation rate in the entire US (inflation: in percentage points change per month, ranging from - 1.92 to 1.22%). These data were taken from January 2003 until May 2012 (n = 113). The result of the regression is shown below:

10. PRACTICE EXAM QUESTION #3 3. An observational study collected the monthly unemployment rate in the entire US (unemployment: in percentage points, ranging from 4.4% to 10%) along with the monthly inflation rate in the entire US (inflation: in percentage points change per month, ranging from -1.92 to 1.22%). These data were taken from January 2003 until May 2012 (n = 113). The result of the regression is shown below: a. What is the correlation between inflation and unemployment? b. What is the formula for the regression line to predict inflation from unemployment? c. June had an unemployment rate of 8.2%. What is the predicted inflation rate for June using this model? d. June had an inflation rate of 0.31%. What is June’s residual value? e. A governmental official sees the results of this regression and states that “a good way to lower the inflation rate is to increase the unemployment rate.” In one or two sentences, please comment on this official’s statement.

11. PRACTICE EXAM QUESTION #3 3. An observational study collected the monthly unemployment rate in the entire US (unemployment: in percentage points, ranging from 4.4% to 10%) along with the monthly inflation rate in the entire US (inflation: in percentage points change per month, ranging from -1.92 to 1.22%). These data were taken from January 2003 until May 2012 (n = 113). The result of the regression is shown below: a. What is the correlation between inflation and unemployment? sqrt(0.0098) = -0.099 (must be negative since the slope is negative) b. (4 points) What is the formula for the regression line to predict inflation from unemployment? c. (4 points) June had an unemployment rate of 8.2%. What is the predicted inflation rate for June using this model? d. (4 points) June had an inflation rate of 0.31%. What is June’s residual value? e. (4 points) A governmental official sees the results of this regression and states that “a good way to lower the inflation rate is to increase the unemployment rate.” In one or two sentences, please comment on this official’s statement.

12. PRACTICE EXAM QUESTION #3 3. An observational study collected the monthly unemployment rate in the entire US (unemployment: in percentage points, ranging from 4.4% to 10%) along with the monthly inflation rate in the entire US (inflation: in percentage points change per month, ranging from -1.92 to 1.22%). These data were taken from January 2003 until May 2012 (n = 113). The result of the regression is shown below: a. What is the correlation between inflation and unemployment? sqrt(0.0098) = -0.099 (must be negative since the slope is negative) b. What is the formula for the regression line to predict inflation from unemployment? Inflation = 0.363-0.022* unemployment c. June had an unemployment rate of 8.2%. What is the predicted inflation rate for June using this model? d. June had an inflation rate of 0.31%. What is June’s residual value? e. A governmental official sees the results of this regression and states that “a good way to lower the inflation rate is to increase the unemployment rate.” In one or two sentences, please comment on this official’s statement.

13. PRACTICE EXAM QUESTION #3 3. An observational study collected the monthly unemployment rate in the entire US (unemployment: in percentage points, ranging from 4.4% to 10%) along with the monthly inflation rate in the entire US (inflation: in percentage points change per month, ranging from -1.92 to 1.22%). These data were taken from January 2003 until May 2012 (n = 113). The result of the regression is shown below: a. What is the correlation between inflation and unemployment? sqrt(0.0098) = -0.099 (must be negative since the slope is negative) b. What is the formula for the regression line to predict inflation from unemployment? Inflation = 0.363-0.022* unemployment c. June had an unemployment rate of 8.2%. What is the predicted inflation rate for June using this model? 0.363-0.022*8.2=0.183 d. June had an inflation rate of 0.31%. What is June’s residual value? e. A governmental official sees the results of this regression and states that “a good way to lower the inflation rate is to increase the unemployment rate.” In one or two sentences, please comment on this official’s statement.

14. PRACTICE EXAM QUESTION #3 3. An observational study collected the monthly unemployment rate in the entire US (unemployment: in percentage points, ranging from 4.4% to 10%) along with the monthly inflation rate in the entire US (inflation: in percentage points change per month, ranging from -1.92 to 1.22%). These data were taken from January 2003 until May 2012 (n = 113). The result of the regression is shown below: a. What is the correlation between inflation and unemployment? sqrt(0.01) = -0.1(must be negative since the slope is negative) b. What is the formula for the regression line to predict inflation from unemployment? Inflation = 0.363-0.022* unemployment c. June had an unemployment rate of 8.2%. What is the predicted inflation rate for June using this model? 0.363-0.022*8.2=0.183 d. June had an inflation rate of 0.31%. What is June’s residual value? Y - Yhat = 0.31 - 0.183 = 0.127 e. A governmental official sees the results of this regression and states that “a good way to lower the inflation rate is to increase the unemployment rate.” In one or two sentences, please comment on this official’s statement.

15. PRACTICE EXAM QUESTION #3 3. An observational study collected the monthly unemployment rate in the entire US (unemployment: in percentage points, ranging from 4.4% to 10%) along with the monthly inflation rate in the entire US (inflation: in percentage points change per month, ranging from -1.92 to 1.22%). These data were taken from January 2003 until May 2012 (n = 113). The result of the regression is shown below: a. What is the correlation between inflation and unemployment? sqrt(0.0098) = -0.099 (must be negative since the slope is negative) b. What is the formula for the regression line to predict inflation from unemployment? Inflation = 0.363-0.022* unemployment c. June had an unemployment rate of 8.2%. What is the predicted inflation rate for June using this model? 0.363-0.022*8.2=0.183 d. June had an inflation rate of 0.31%. What is June’s residual value? Y - Yhat = 0.31 - 0.183 = 0.127 e. A governmental official sees the results of this regression and states that “a good way to lower the inflation rate is to increase the unemployment rate.” In one or two sentences, please comment on this official’s statement. Causality is not the same as correlation. The regression result just shows linear correlation between inflation rate and unemployment rate. But we cannot draw a causal conclusion from that (since it is an observational study).