The table shows how many miles Jack ran per week for weeks one through nine.
x y
1 3
2 5
3 6
4 9
5 10.5
6 13
7 15
8 16
9 19
Question:
a. Use the table to plot the points.
b. Describe the correlation, including whether it is strong or weak.
c. Draw a line of best fit.
d. Write the equation of a line of best fit in slope-intercept form.
e. Using the line of best fit, estimate how may miles Jack ran the 10th week; show work.
f. During which week would you expect Jack to run a full marathon, 26.3 miles? Do you think that you should round up or down to the nearest week? Why?
We need the answers for d-f
What the answer to the problems
a. To plot the points, you can use a coordinate plane. The "x" values will be plotted on the horizontal axis and the corresponding "y" values will be plotted on the vertical axis. Each point represents the week and the number of miles Jack ran.
b. To determine the correlation, you need to analyze how the points are distributed on the scatterplot. If the points roughly form a straight line, it indicates a positive or negative correlation. If the points are scattered and do not follow a clear pattern, it indicates a weak or no correlation. You can also calculate the correlation coefficient to quantify the strength of the correlation.
c. To draw a line of best fit, you need to visually estimate the trend in the scatterplot. It should pass through the majority of the points and represent the overall pattern. It should not be skewed or biased by a few extreme points.
d. The equation of a line of best fit can be written in slope-intercept form, which is y = mx + b. Here, "m" represents the slope of the line and "b" represents the y-intercept. To calculate the equation, you can use the slope formula and substitute the values of any two points from the scatterplot.
e. Using the line of best fit, you can estimate how many miles Jack ran in the 10th week by substituting the week number (10) into the equation. This will give you the estimated value of "y," which represents the number of miles.
f. To determine the week at which Jack would run a full marathon (26.3 miles), you can again substitute the miles (26.3) into the equation of the line. This will give you the estimated week. In terms of rounding, it would be appropriate to round up to the nearest week since running a full marathon typically requires training and preparation, suggesting that it may not happen exactly on a particular week.
Please note that for accurate and precise calculations, a statistical software or graphing calculator might be helpful.