Section 1.4 Curve Fitting with Linear Models

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Presentation transcript:

Section 1.4 Curve Fitting with Linear Models Algebra 2 Section 1.4 Curve Fitting with Linear Models

Warm-up Write the equation of the line passing through each pair of points in y=mx+b form. (5,-1) and (0,-3) (8,5) and (-8,7) Use the equation 𝑦=−0.2𝑥+4. Find x for each given value of y. y=7 y=3.5

We could graph the most recent math and science grades for all students in the class in a scatter diagram.

Definitions Regression- the statistical study of the relationship between variables. Correlation- the strength and direction of the linear relationship. Line of best fit- line that best fits the data Correlation coefficient- (r) is a measure of how well the data fits the model.

A study may show that there is a correlation between a person’s level of education and the amount of money they make.

Can you think of pairs of things (using numbers) that can be related?

If both variables increase, we say there is a positive correlation. If one variable increases while the other decreases, we say there is negative correlation. If there appears to be no relationship between the two variables, we say there is no correlation.

If there is a strong linear relationship ( positive or negative, a line of best fit can be used to make predictions.

The correlation coefficient tells you how well the data fits a line of best fit. r=0 means there is no correlation r=1 means the data set forms a line with a positive slope r= -1 means the data set forms a line with a negative slope

Correlation coefficients fall somewhere in the middle Between -1 and +1, inclusive.

r values close to 1 or -1 indicate a strong correlation r values close to 0 indicate a weak correlation

Classwork/homework #4 Pg. 36 3,4 Use these directions Make a scatter plot Draw a line of best fit through your points Mark two points on the line Use those two points to write the equation of a line