In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player. Let y represent the home run percentage (number of home runs per 100 times at bat). Suppose a random sample of baseball players gave the following information. Given the scatter diagram and "best fit" line for the data below, would you say the correlation is low, moderate, or strong? Positive or negative
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The more it approximates a straight line, the stronger the correlation.
If it goes from lower left to upper right, it is positive. If it goes from upper left to lower right, it is negative.
To determine if there is a linear correlation between batting average and home run percentage, we need to analyze the scatter diagram and the "best fit" line for the given data.
First, let's plot the data points on a scatter plot, with the batting average (x-axis) and home run percentage (y-axis). Once we have the scatter plot, we can visually assess the relationship between the variables.
To obtain the "best fit" line, we can use a statistical technique called linear regression. This technique allows us to find the line that best represents the relationship between the variables by minimizing the overall distance between the line and the data points.
Once we have the scatter plot and the "best fit" line, we can interpret the correlation by examining the direction and strength of the relationship.
If the "best fit" line has a positive slope (going upward from left to right), it indicates a positive correlation, meaning that as the batting average increases, the home run percentage tends to increase as well. On the other hand, if the slope is negative (going downward from left to right), it suggests a negative correlation, meaning that as the batting average increases, the home run percentage tends to decrease.
To assess the strength of the correlation, we look at how closely the data points cluster around the "best fit" line. If the data points predominantly lie close to the line, it suggests a strong correlation. If the data points are more scattered and do not conform closely to the line, it indicates a weak correlation. Additionally, the extent to which the values of the correlation coefficient are close to either -1 or 1 can give us an idea of the strength of the correlation.
Analyzing the scatter diagram and the "best fit" line for the given data, you can make an assessment of whether the correlation is low, moderate, or strong, and whether it is positive or negative, based on the criteria outlined above.