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QuestionA golfer has data on clubhead speeds (mph) and distances (yards) for 20 games. What analysis should be done: correlation, averages, or something else?

Studdy Solution

STEP 1

Assumptions1. The data provided includes clubhead speeds in mph and corresponding distances in yards for20 games. . The data is accurate and reliable.
3. The user is seeking assistance with this data but has not specified a particular mathematical operation.

STEP 2

Given the nature of the data, there are several mathematical operations that could be performed. These include1. Calculating the average clubhead speed and average distance.
2. Finding the correlation between clubhead speed and distance. . Performing a regression analysis to predict distance based on clubhead speed.

STEP 3

To calculate the average clubhead speed and average distance, we would sum up all the speeds and distances respectively and then divide by the number of games.
For average clubhead speedAverage Speed=Sum of SpeedsNumber of GamesAverage\, Speed = \frac{Sum\, of\, Speeds}{Number\, of\, Games}For average distanceAverage Distance=Sum of DistancesNumber of GamesAverage\, Distance = \frac{Sum\, of\, Distances}{Number\, of\, Games}

STEP 4

To find the correlation between clubhead speed and distance, we would use the formula for Pearson's correlation coefficient. This measures the strength and direction of association between two continuous variables.
r=n(Σxy)−(Σx)(Σy)[nΣx2−(Σx)2][nΣy2−(Σy)2]r = \frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2 - (\Sigma x)^2][n\Sigma y^2 - (\Sigma y)^2]}}Where- n is the number of pairs of scores- Σxy is the sum of the products of paired scores- Σx is the sum of x scores- Σy is the sum of y scores- Σx² is the sum of squared x scores- Σy² is the sum of squared y scores

STEP 5

To perform a regression analysis, we would use the least squares method to fit a line to the data. This line can then be used to predict distance based on clubhead speed. The formula for the line isy=mx+by = mx + bWhere- y is the predicted distance- m is the slope of the line- x is the clubhead speed- b is the y-interceptThe slope and y-intercept can be calculated using the formulasm=n(Σxy)−(Σx)(Σy)nΣx2−(Σx)2m = \frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{n\Sigma x^2 - (\Sigma x)^2}b=Σy−m(Σx)nb = \frac{\Sigma y - m(\Sigma x)}{n}

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