1. Given below are the winning times (in seconds) for the men’s 1500 meter run in the Olympics. Enter the data into two columns of a spreadsheet. Label the columns "Year" and "Time".

   YEAR	TIME
   1900	246.0
   1904	245.5
   1908	243.4
   1912	236.8
   1920	241.8
   1924	233.6
   1928	233.2
   1932	231.2
   1936	227.8
   1948	229.8
   1952	225.2
   1956	221.1
   1960	215.6
   1964	218.1
   1968	214.9
   1972	216.3

2. Calculate the linear correlation coefficient: r by using the CORREL( ) function.
3. Create a Scatter Plot of winning race Time on the Vertical axis versus Year of the Olympics on the Horizontal axis.
4. Overlay the scatter plot with the Linear Regression L ine (called Trendline in Excel) of best fit.
5. Determine the Slope and y-Intercept of this line. Use the Excel functions SLOPE() and INTERCEPT() .

Questions about C orrelation :

1. What is the value of the correlation coefficient? Why is it negative?
2. A strong linear correlation for a sample of this size is when |r| > 0.5 Based upon this criteria, are the race Times strongly correlated to the Year of the Olympics?
3. When there is a strong correlation, a linear equation can be expected to make good predictions when doing "interpolations", and less accurate predictions when doing an "extrapolation". Predictions of race time for which year: 1940 or 1980 would be an interpolation, and for which year would be an extrapolation?
   Questions about Scatter Plot:
4. What is the visual appearance of the clustering pattern of points in the scatter plot: Nearly circular (no correlation), Somewhat oval (slight correlation), Elongated and narrow oval (strong correlation), or Very nearly linear (very strong correlation)?
5. What is the trend in winning times for the 1500 meter race as the Olympics move forward in years?
   Questions about Linear Regression Line and Equation :
6. What is the slope of the regression line? What are the units of this number (use the units of the variables in the equation to give a what? per what? answer)? The value of the slope in the regression equation tells us that the race times are changing by how much from Olympic to Olympic (Careful! The Olympics are four years apart) ?
7. Write the regression equation in the slope-intercept form:
   Time = <slope> Year + <intercept>.
8. World War II interrupted the Olympics. Use the regression equation to predict what the winning Times for the Years: 1940 and 1944 might have been.
9. Predict winning Times for the Years: 1976 and 1980 which are beyond the range of the data in the table. From records books, the actual winning Times were 219.2 and 218.4 seconds in Years 1976 and 1980 respectively. Calculate the "residual error" for each of these last two predictions. Residual error is the difference between predicted and actual. Give a positive error answer if predicted is greater than actual, and negative if predicted is less than actual.
10. Why is the intercept value of the regression equation different from where the regression line appears to intercept (cross over) the left edge of Excel’s Scatter Plot ?
11. If a future runner could run at an average of 30 MPH for the entire distance, they could finish in 111.8 seconds! In what Y ear does the regression equation predict this will happen ?

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