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). A random sample of n = 7 professional baseball players gave the following information.x 0.267 0.326 0.253 0.298 0.245 0.305 0.304y 3.1 6.8 3.8 5.4 1.5 6.0 3.7Σx = 1.998; Σy = 30.3; Σx2 = 0.575844; Σy2 = 151.39; Σxy = 8.9374 (a) Find Se. (Round your answer to three decimal places.) (b) Find r. (Round your answer to three decimal places.) Test that ρ is positive. Use α = 0.01. (Round your answers to three decimal places.)t = critical t = Conclusion:At the 1% level of significance, there is sufficient evidence to conclude that the population correlation coefficient is greater than zero.At the 1% level of significance, there is insufficient evidence to conclude that the population correlation coefficient is greater than zero. (c) Find b. (Round your answer to three decimal places.) Test that β is positive. Use α = 0.01. (Round your answers to three decimal places.)t = critical t = Conclusion:At the 1% level of significance, there is sufficient evidence to conclude that the slope of the population least-squares line is positive.At the 1% level of significance, there is insufficient evidence to conclude that the slope of the population least-squares line is positive. (d) Find the equation of the least-squares line ŷ. (Round your answers to three decimal places.)ŷ = + x Find a 90% confidence interval for the predicted home run percentage for a player with a batting average of 0.310. (Round your answers to three decimal places.)to
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
In baseball, is there a
x 0.267 0.326 0.253 0.298 0.245 0.305 0.304
y 3.1 6.8 3.8 5.4 1.5 6.0 3.7
Σx = 1.998; Σy = 30.3; Σx2 = 0.575844; Σy2 = 151.39; Σxy = 8.9374
(a) Find Se. (Round your answer to three decimal places.)
(b) Find r. (Round your answer to three decimal places.)
Test that ρ is positive. Use α = 0.01. (Round your answers to three decimal places.)
t =
critical t =
Conclusion:
At the 1% level of significance, there is sufficient evidence to conclude that the population
At the 1% level of significance, there is insufficient evidence to conclude that the population correlation coefficient is greater than zero.
(c) Find b. (Round your answer to three decimal places.)
Test that β is positive. Use α = 0.01. (Round your answers to three decimal places.)
t =
critical t =
Conclusion:
At the 1% level of significance, there is sufficient evidence to conclude that the slope of the population least-squares line is positive.
At the 1% level of significance, there is insufficient evidence to conclude that the slope of the population least-squares line is positive.
(d) Find the equation of the least-squares line ŷ. (Round your answers to three decimal places.)
ŷ =
+
x
Find a 90% confidence interval for the predicted home run percentage for a player with a batting average of 0.310. (Round your answers to three decimal places.)
to
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 2 images
