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MATH 225N WEEK 8 ASSIGNMENT
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MATH 225N WEEK 8 ASSIGNMENT
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MATH 225N WEEK 8 ASSIGNMENT: CORRELATION ANDCAUSATION CORRECT ANSWERS / ALREADY GRADED A
correlation - ANSWER: numerical measure of the strength and direction of a linear
relationship between two numerical variables
real life examples of correlation - ANSWER: - height and weight
- outdoor temperature and cost of heating
- amount of coffee consumed and level of intelligence
- amount of time spent on a project and amount of time spent on leisure
sports examples of correlation - ANSWER: - players performance and team
performance
- team performance and stadium attendance
- ticket price and stadium attendance
- number of assists and number of field goals made
correlation analysis - ANSWER: statistical method used to discover if there is a
relationship between two variables and how strong that relationship may be
three types of correlation coefficients - ANSWER: - Pearson product-moment
coefficient (Pearson's r)
- Spearman's rank correlation coefficient (Spearman's p: rho)
- Kendall rank correlation coefficient (Kendall's T: tau)
scatter diagram method of correlation - ANSWER: the closer your data points are to
the line, the higher the absolute value of the correlation coefficient and the stronger
your linear coefficient
covariance - ANSWER: - the variance shared by two variables
- ranges from negative infinity to positive infinity
- only reflects the direction of the relationship
correlation coefficient (r) - ANSWER: - unitless measure of the relationship between
variables
- measures both the strength and direction of a relationship
- makes it possible to directly compare coefficients between studies or datasets
- ranges from -1 to 1
Pearson Product-Moment Coefficient (Pearson's r) - ANSWER: - most commonly used
correlation coefficient
- measure of the linear relationship between two (continuous variables)
assumptions of the Pearson's r - ANSWER: - each variable should be continuous
- two variables should be paired
, - there should be no outliers in either variable
- a straight-line relationship between the variables should be formed
Pearson's r formula - ANSWER: - numerator: covariance of two variables
- denominator: product of standard deviation of two variables
Spearman's Rank Correlation Coefficient - ANSWER: - most common alternative to
Pearson's r
- measure of the monotonic (but not linear) relationship between two variables
correlation coefficient vs. regression coefficient - ANSWER: - two commonly used
measures to investigate the relationship between variables
- correlation quantities the strength and direction of the linear relationship between
two variables
- regression expresses the relationship between two variables in the form of an
equation
what does the coefficient of determination (R squared) represent - ANSWER:
goodness of fit
baseball's pythagorean theorem formula - ANSWER: (runs scored)^2/(runs scored)^2
+ (runs allowed)^2
purpose of the baseball pythagorean theorem - ANSWER: used to estimate the
team's expected winning percentage based on number of runs scored and allowed
ideal exponent for baseball - ANSWER: 1.83
runs created - ANSWER: statistic used to estimate a player's offensive contribution
by quantifying their ability to generate runs for their team
limitations of runs created - ANSWER: - linear assumption
- limited context
- excludes non-offensive contributions
- not adjusted for external factors
- challenge in translation between teams and players
BA formula - ANSWER: hits/at bats
OBP formula - ANSWER: (hits + base on balls + hit by pitch)/(at bats + base on balls +
hit by pitch + sacrifice fly)
SLG formula - ANSWER: total bases/at bats
OPS formula - ANSWER: on base percentage + slugging percentage
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