# data[].attributes.body
Due Thurs. May 11 at beginning of class.

# data[].attributes.attachment_link.title
Algebra 1 CP Quarter 4 Extra Credit Opportunity (2)

# data[].attributes.headline
Review these example before class Thursday

# data[].attributes.subject
Review these example before class Thursday

# data[].attributes.headline
FYI: Correlation Coefficient vs. Coefficient of Determination

# data[].attributes.subject
FYI: Correlation Coefficient vs. Coefficient of Determination

# data[].attributes.attachment_link.readable_text
How well does your regression equation truly represent
your set of data?
One of the ways to determine the answer to this question is to
exam the correlation coefficient and the coefficient of determination.

Correlation Coefficient, r :

(Aren't you glad you have a graphing calculator that computes this formula?)value of Positive values Negative values A value near zero means that there is a random, nonlinear relationship A A correlation greater than 0.8 is generally described as These values can vary based upon the The quantity r, called the linear correlation coefficient, measures the strength and
the direction of a linear relationship between two variables. The linear correlation

indicate a relationship between
indicate a relationship between
between the two variables Note that perfect correlation of 1 occurs only when the data points all lie exactly on a strong, whereas a correlation
"type" of data being examined. A study utilizing scientific data may require a stronger
correlation than a study using social science data.
less than 0.5 is generally described as weak.
straight line. If r = +1, the slope of this line is positive. If r = -1, the slope of this
line is negative. ris a dimensionless quantity; that is, it does not depend on the units
employed.

No correlation: If there is no linear correlation or a weak linear correlation, r is
close to 0. x and y such that as values for x increase, values
for y decrease.
Negative correlation: If x and y have a strong negative linear correlation, r is close
to -1. An rvalue of exactly -1 indicates a perfect negative fit. x and y variables such that as values for x increases,
values for y also increase.
The mathematical formula for computing r is:

where n is the number of pairs of data.

The r is such that -1 < r < +1. The + and signs are used for positive
linear correlations and negative linear correlations, respectively.
Positive correlation: If x and y have a strong positive linear correlation, r is close
to +1. An rvalue of exactly +1 indicates a perfect positive fit.
coefficient is sometimes referred to as the Pearson product moment correlation coefficient in
honor of its developer Karl Pearson.

Coefficient of Determination, r 2 orR 2 :

The is useful because it gives the proportion of . It is a measure that allows us to determine how certain one can be in makingFor example, if coefficient of determination, r
the variance (fluctuation) of one variable that is predictable from the other variable

predictions from a certain model/graph.
The coefficient of determination is the ratio of the explained variation to the total
variation.
The coefficient of determination is such that 0 < r 2 < 1, and denotes the strength
of the linear association between x and y.
The coefficient of determination represents the percent of the data that is the closest
to the line of best fit.
r = 0.922, then r ² = 0.850, which means that
85% of the total variation in y can be explained by the linear relationship between x
and y (as described by the regression equation). The other 15% of the total variation
in y remains unexplained. The coefficient of determination is a measure of how well the regression line
represents the data. If the regression line passes exactly through every point on the
scatter plot, it would be able to explain all of the variation. The further the line is
away from the points, the less it is able to explain. ²,

# data[].attributes.attachment_link.keywords[]
graphing calculator ti-83+ math b statistics correlation coefficient and coefficient of determination

# data[].attributes.attachment_link.title
Statistics 2 - Correlation Coefficient and Coefficient of Determination

# data[].attributes.attachment_link.description
How well does your regression equation truly represent your set of data? One of the ways to determine the answer to this question is to exam the correlation coefficient and the coefficient of determination.

# data[].attributes.attachment_link.keywords[]
graphing calculator ti-83+/84+ exponential regression model

# data[].attributes.attachment_link.title
Statistic 2 - Exponential Regression Model

# data[].attributes.attachment_link.description
Statistics 2 - Comparing Exponential Regression Model

# data[].attributes.attachment_link.keywords[]
graphing calculator ti-84+ statistics quadratic regression

# data[].attributes.attachment_link.title
Statistics 2 - Quadratic Regression Model Example

# data[].attributes.attachment_link.description
Statistics 2 - Quadratic Regression Model Example