CAS MA 416 Lecture 3: MA416 Class 3

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erinbadger658

14 Feb 2017

School

Boston University

Department

Mathematics & Statistics

Course

CAS MA 416

Professor

Joe Massaro

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Document Summary

Ma416 class 3: the correlation coefficient r (sample correlation), (population) The correlation coefficient measures how closely the points of the scatter plot fall along the regression line (sort of ). It is not a measure of the steepness of the regression line. The correlation coefficient is a standardized measure that is independent of the scale of x or y; the correlation between height and weight is the same whether weight is measured in pounds, ounces, grams, kilograms, etc. Correlation is non-directional, measuring the mutual association between two measurement variables (unlike regression, which is implies a direction to the association with the independent and dependent variable). R close to 0 indicates little or no association. The numerators of the slope and r are the same; r=0 if and only if (cid:2869) =0. Formulas relating the slope from a regression line to the correlation coefficient: rpopulation = 0.

Related Questions

Identify the true statements about the correlation coefficient, r.

a.) The correlation coefficient is not affected by outliers.

b.)The value of r ranges from negative one to positive one.

c.) When the data points in a scatter plot fall closely around a straight line that is either increasing or decreasing, the correlation between the two variables is strong.

d.) A correlation coefficient of zero means that no relationship exists between the two variables.

e.) If two variables are positively correlated, when one variable increases, the other variable decreases.

f.) The sign of r describes the direction of the association between two variables.

bluefly693

Average price per square foot of floor area in new one-family houses sold. Price per square foot of floor area excludes value of improved lot Source: Year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Price per square foot $55.18 $57.41 $60.21 $62.45 $64.38 $66.81 $67.83 $67.70 $70.43 $71.93 $75.68 $79.21 $85.13 $90.63 $91.99 Instead of working on portions of the scatter plots, we want to approximate the data by a line we can use to predict prices in the future. The line that will best fit the given data is called the linear regression. The approximation will be acceptable whether the determina- tion coefficient R (r**2) is close to 1 or the correlation coefficient r is close to -1 or +1.

a) using your entered data to find the equation y = ax + b of the best line through the data points and give the values of coefficients a and b, and of the determination coefficient R or correlation coefficient r.

b. Use Excel to plot the scatter plot and the regression line on the same graph.

c. Is the linear regression a visually good approximation of the data? Sustain your argument by a mathematical proof.

d. use the linear regression to predict the price per square foot area in 2009 e. In what year will the price per square foot be greater than $199?

sangriaelk229

1.) In a simple linear regression problem, r and b1:
A) must have opposite signs.
B) may have opposite signs.
C) must have the same sign.
D) are equal.

2.) The sample correlation coefficient between X and Y is 0.375. It has been found that the p-value is 0.256 when testing H0 : ? = 0 against the two-sided alternative H1 : ? ? 0. To test H0 : ? = 0 against the one-sided alternative H1 : ? < 0 at a significance level of 0.2, the p-value is:
A) 0.256/2
B) 1 - 0.256/2
C) (0.256)2
D) 1 - 0.256

copperlocust228

CAS MA 416 Lecture 3: MA416 Class 3

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