1 / 32

“I just got lost in thought. It was unfamiliar territory”

Math Review #2. “What happens if you get scared half to death twice?”. “I just got lost in thought. It was unfamiliar territory”. Math Review Friday June 4 2003. Introduction Symbols Operations Central Tendencies Linear Algebra Correlation/Regression Analysis

zoltan
Download Presentation

“I just got lost in thought. It was unfamiliar territory”

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Math Review #2 “What happens if you get scared half to death twice?” “I just got lost in thought. It was unfamiliar territory”

  2. Math ReviewFriday June 4 2003 • Introduction • Symbols • Operations • Central Tendencies • Linear Algebra • Correlation/Regression Analysis • System of Equations: Linear/Quadratic • Applied Calculus

  3. Basic Math Review Operations Why logarithms? Power and product rules: logb(xy) = logb(x) + logb(y) logb(xn) = nlogb(x) These rules motivated the introduction of logarithms (by Napier, in early 17th Century) and motivated their use in scientific computation until… computers!

  4. Basic Math Review Operations Why logarithms? Example: Calculate First use logs, then use log tables: y = 75/ 212 Log y = Log (218/ 75) http://www.sosmath.com/tables/logtable/logtable.html

  5. Basic Math Review Operations Solve for x: ln(ea) = bx Solve for y using common logarithms (base 10): y = 175 Find the exponent of 10 that solves for x: x2 = 5.5.10-12

  6. Basic Math Review Central Tendencies The most commonly used descriptive statistics are measures of central tendency The sample mean (: pronounced “x bar”) is: Where Sxi represents the sum of all values in the sample and n represents the sample size

  7. Basic Math Review Central Tendencies • Mean: arithmetic average • Median: middle value of a set of values • Mode: the data value that occurs most often

  8. Basic Math Review Central Tendencies Let’s assume we have a student population (n = 47) But what happens if we have an outlier (skewed distribution )?

  9. Basic Math Review Central Tendencies Let’s assume we have a real student population

  10. Basic Math Review Linear relationships Let’s play… Starbucks anyone?

  11. Basic Math Review Linear Relationships

  12. Basic Math Review Linear Algebra The “slope” (m) of a line is its rate of change: Slope: Dy/Dx or (y2-y1)/(x2-x1)

  13. Basic Math Review Linear Realtionships The “intercept” (b) of a line is the point where x = 0

  14. Basic Math Review Linear Relationships The function f(x) = y = mx + b You can use it to make predictions

  15. Basic Math Review Graphing Linear Relationships Let’s assume we have a real fish population Any question regarding this data set?

  16. Basic Math Review Correlation The sample mean is: Sum of squares for variable x. This statistics quantifies the spread of variable x:

  17. Basic Math Review Correlation Sum of squares for variable y. This statistics quantifies the spread of variable y:

  18. Basic Math Review Correlation Sum of the cross-products. This statistics is analogous to the other sums of squares except that it quantifies the extent to which the two variables go together or apart:

  19. Basic Math Review Correlation Fish Data: SSxx: 78.5 SSyy: 182.0 SSxy: 113.8 The correlation coefficient is: Here r = 0.95

  20. Basic Math Review Correlation: Fish Data The correlation coefficient is positive

  21. Basic Math Review Correlation: the correlation coefficient has no inherent value, and in the exception of strong relationships as in the case presented, r is hard to use to determine correlational strength. Another statistics is much more useful: the coefficient of determination (r2)

  22. Basic Math Review Correlation: Here r2 = 0.91 This statistic quantifies the proportion of the variance of one variable that is explained by the other – Functional?

  23. Basic Math Review Linear Algebra Forgot a section of the fish data set

  24. Basic Math Review Correlation: Here r2 = 0.82

  25. Basic Math Review Whole data set

  26. Basic Math Review Correlation: Linear?

  27. Basic Math Review Non-linear relationship

  28. Basic Math Review Non-linear relationship Let’s make a statements about the relationship: -) The weight is  to the volume W  V Where: V = A x L A = ax L2 V = ax L3 W = rx V Therefore W = axrx L3

  29. Basic Math Review Non-linear relationship W = axrx L3

  30. Basic Math Review Non-linear relationship

  31. Log L = Log (k x W1/3) Log L = Log k + 1/3 Log W y = b + mx

  32. Monday • Lamont orientation (LDEO Exec. Director and DEES Chair) • Math Review #3: System of Equations: Linear/Quadratic - Applied Calculus

More Related