MATH SOLVE

9 months ago

Q:
# The graph below plots the values of y for different values of x:plot the ordered pairs 1, 1 and 2, 4 and 3, 7 and 4, 9 and 5, 12 and 6, 16Which correlation coefficient best matches the data plotted on the graph? β0.5 0 0.25 0.90

Accepted Solution

A:

Solution:Plotting the Ordered pairs on coordinate plane (1, 1) , (2, 4) , (3, 7) , (4, 9) , (5, 12) and (6, 16).A line of best fit is the line which passes through few points, one point or more than one point of the set of given ordered pairs.As, you can see line of best fit passes through four points.Equation of line of best fit can be arrived with the help of two point slope form of line.[tex]\frac{y-1}{x-1}=\frac{4-1}{2-1} \\\\ y-1= 3 x - 3 \\\\ y= 3 x - 2[/tex]The formula used here is two point slope form of line:[tex]\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]As you can see that Points on the coordinate plane are very close to Line of best fit.So, there are chances of perfect positive correlation.Option (D) 0.90 is true description of correlation between two variables.