AI HL: Regressions Overview (4.4,4.10,4.12)

​Regressions Overview

By Benito Toscano

Match

DO NOW: Match each function to its general form.

• y=mx+c

• y=ax^2+bx+c

• y=ab^x

• y=ax^b

• y=a+bln(x)

Linear

Quadratic

Exponential

Power

Logarithmic

• Linear

• Quadratic

• Exponential

• Power

• Logarithmic

LO and DoL

LO: Students will determine the curve of best fit using various regressions and use these curves to make predictions.

DoL: Students will complete a multi-part, IB-Style problem over regressions with at least 80% accuracy

Form of y=mx+c

CALC STEPS: Data in Spreadsheet => Menu => Stat => Stat Calc => Linear Regression (mx+b)

​Linear Regression

Open Ended

Write the equation of the regression LINE for the following data in the form y=mx+c. Round all coefficients to three sig figs.

A value that tells you strength of correlation (strong or weak), and which DIRECTION the variables are correlated (positive or negative)

​Correlation Coefficient

Open Ended

Write the value of the correlation coefficient for the previously calculated line of best fit. Round to three sig figs.

Open Ended

Why do you think this exemplar is two marks?

Draw

Circle where they are awarding marks on here.

Multiple Choice

Hence, our data has a ___________ __________ correlation.

• Strong Positive

• Weak Positive

• Weak Negative

• Strong Negative

Draw

Circle where they are awarding marks on here.

Open Ended

​REMEMBER!

For all regressions it is important to keep track of which measurement is attached to which variable.

Match

Match each measurement to its variable

• Weight

• Height

• Mr. T

X

Y

The best math teacher you've ever had

• X

• Y

• The best math teacher you've ever had

Multiple Choice

We want to predict how tall someone who weighs 175 pounds would be. We would substitute 175 in for...

• x

• y

Open Ended

Hence, the predicted height for someone with a weight of 175 pounds would be....

Open Ended

Now, predict the weight for someone that is 5 foot 10 and a half.

Open Ended

Where are the two marks coming from on this exemplar?

From your EdPuzzle

​

​Other types of regressions!

Open Ended

Which regression type do you think will cause you the most issues on the exam?

Multiple Select

Which do you think best fits this data set?

• Quadratic

• Cubic

• Exponential

• Sinusoidal

Draw

Circle the words that are most important for this problem.

Open Ended

Open Ended

Where do you think the marks are coming from on this question? Three total!

Between 0 and 1

A measure of how well our chosen model fits the data set

​

​Coefficient of Determination

Open Ended

Which would have a bigger coefficient of determination? Why?

Open Ended

Write down the coefficient of determination for the cubic regression curve from before.

Draw

Where is the one mark coming from? Annotate the exemplar.

Open Ended

Using the cubic model from before, predict the y-value for an x-value of 5.

Mr. T been hiding something....

Numerical Solve Function

Calculator => Menu => Algebra => Numerical Solve



Disclaimer: Only gives one answer though. Use graph for something that should have multiple answers.

Open Ended

Using the cubic model, predict the x-value for a y-value of 10.

​Spearman's Rank Correlation

R-Value between RANKS

Draw

Complete the rankings for this data

Draw

Circle where the marks come from on this ranking exemplar.

Ties in ranks!

Figure out which places they are tied for.

Average these ranks.

They get the same rank!

Draw

Rank this data.

Open Ended

When finding ranks, Kalino accidentally read the Netherlands' score as 478. Why wouldn't this affect Spearman's rank correlation coefficient?