Chapter 12 More About Regression Let’s look at the Warm-Up first to remind ourselves what we did with regression! Remember FODS!

Section 12.1 Inference for Linear Regression

Confidence intervals and significance tests about the slope of the population regression line are based on the sampling distribution of b, the slope of the sample regression line.

Conditions - LINER

How it works…

Confidence Intervals

Let’s look at SE…

Hypothesis Tests

Let’s do a confidence interval! We examined data from a study that investigated why some people don’t gain weight even when they overeat. Researchers deliberately overfed a random sample of 16 healthy young adults for 8 weeks. They measured fat gain and change in energy use from activity other than deliberate exercise (non-exercise activity, NEA) – fidgeting, daily living, etc – for each subject. Here are the results: NEA Change (cal) Fat Gain (kg) NEA Change (cal) Fat Gain (kg)

Construct and interpret a 90% confidence interval for the slope of the population regression line. Check conditions first! Type information into calculator! Linear – look at scatterplot and draw it to prove that you have checked this condition. Independent – Normal – look at Normal probability plot of residuals and draw it to prove you checked this condition. (find the LinReg first and then do NPP with RESID – 2 nd list)

Keep checking conditions… Equal Variance – we want the standard deviation (the average distance from the mean – or 0) to be the same for all points – draw the residual plot to prove that you have looked at it. Random –

Do:

A Significance Test… Infants who cry easily may be more easily stimulated than others. This may be a sign of higher IQ. Researchers explored the relationship between crying infants 4 to 10 days old and their later IQ scores. The researchers flicked the infants with a rubber band and recorded the crying. They measured its intensity by the number of peaks in the most active 20 seconds. The table below contains data from a random sample of 38 infants.

a) Here is a scatterplot of the data with the least-squares regression line added. Describe what this graph tells you about the relationship between these two variables.

b) Using the min-tab output, what is the equation of the least-squares regression line?

c) Interpret slope and y-intercept of the regression line in context

d) Do these data provide convincing evidence that there is a positive linear relationship between crying counts and IQ scores in the population of infants?

Homework Pg 759 (6, 8, 13-15, 18-26)