Question

a baseball teams total home runs and wins over the last eight years is recorded below

11.) make a scatter plot of the data above with home runs as the independent variable. find the equation of the line of best fit. round coefficients and constants to the nearest hundredth.
( y = 1.82x + 326.23 )
( y = 0.43x - 28.01 )
( y = 0.32x )
( y = 0.25x + 18.21 )
( y = 0.51x - 46.25 )

find the correlation coefficient, rounded to the nearest hundredth.

what kind of relationship does the correlation coefficient show?
a. strong positive
b. strong negative
c. weak positive
d. weak negative

predict the baseball teams wins if they hit 204 home runs next year.
a. 76
b. 32
c. 63
d. 79
e. 60

Explanation:

Step1: Input data into calculator

Input home - runs (x) and wins (y) data into a graphing calculator or statistical software.

Step2: Calculate line of best fit

Using the linear regression function, we find that the equation of the line of best fit is \(y = 0.43x-28.01\).

Step3: Calculate correlation coefficient

Using the same data and correlation coefficient function in the calculator, \(r\approx0.91\) (strong positive).

Step4: Predict wins for \(x = 204\)

Substitute \(x = 204\) into \(y=0.43x - 28.01\):

$$
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$$

Answer:

Equation of line of best fit: \(y = 0.43x-28.01\), Correlation coefficient: \(r\approx0.91\) (A. Strong Positive), Prediction for \(x = 204\): E. 60