chapter 27 part 1 inferences for regression. yearrate 19710.08 19740.10 19750.13 19780.15 19810.18...

CHAPTER 27 PART 1

Inferences for Regression

Year Rate1971 0.081974 0.101975 0.131978 0.151981 0.181981 0.201985 0.221988 0.251991 0.291995 0.32

This table lists postal rates for first class mail, gathered by the US Postal Service.

1)Make a scatterplot. 2)What type of relationship is shown

in the scatterplot? 3)What is the correlation? What does

that mean? 4)What is and what does it mean? 5)Give a linear model. 6)Interpret the slope and y-intercept.7)Is the linear model appropriate?

We want to know if the association in our sample provides evidence that there must be an association between the two variables in the population.

Assumptions and Conditions for Inferences by Regression

Read about these on pages 651-653. There are a lot of

them.

The slope of the regression line for all

possible samples follows a t-model with n-2 degrees

of freedom.

In TI-84 Calculator:

STAT TESTS F:LinRegTTest

How to get t-score and P-value

In TI-84 Calculator:

STAT TESTS G:LinRegTInt

How to get a Confidence Interval

Using the data from your worksheet (Anxiety Level and Math Test), perform a hypothesis test and

create a 95% confidence interval for slope for the anxiety and math test

data.

STATTESTF:LinRegInt

With a P-value of 0.0084, we reject the null hypothesis stating that there is no association between math test scores and anxiety level. There is strong evidence that, on average, lower anxiety level is associated with higher math scores.

𝑡=−2.89 𝑎𝑛𝑑𝑃=0.0084

STATTESTG:LinRegInt

(−7.702 ,−1.271)We are 95% confident that the interval (-7.702, -1.271) contains the average math test score difference associated with difference in anxiety level. Each additional unit of anxiety level is associated with an average decrease of between 1.271 and 7.702 points on the math test.

Today’s Assignment: Page 673 #2 and worksheet Read about conditions &

assumptions – we will use these tomorrow