Unit 9- confidence interval for slope of a regression model

3 conditions for the confidence interval and significant test for slope of linear regression line

1. The true relationship between x and y is linear- scatter plot needs to look linear and residual plot has no patterns

2. The standard deviation of y (oy), does not vary with x- look for that fact the the reponse variable seems to vary by similar amount of times for the explanatory variable

3. For a particular value of x, the reposes’s (y-values) are approximately normally distributed- the dotplot of residuals is roughly symmetic, single-peaked, and somewhat bellshaped

when the population regression model: uy= a+ slope x meets the condtions, the sampling distribution of the slope b of the sample regression has

S: Shape is approximately Nomral

Center: of sampling distribution is the slope of population

V: standard deviation standard deviation of residual fo the population regression line/standard deviation of x values in the population, n is the sample size

(NEED TO CHECK THE SAMPLE SIZE IS LESS THAN 10% OF POPULATION SIZE

CONFIDENCE INTERVAL FOR SLOPE ACRONYM(LINER) + conclusion

L- LINEAR RELATIONSHIP- dufs the scatter plot and look at residual plot to describe

I- INDEPENDENT- 10% CONDITION

N- NORMAL- LOOK AT DOTPLOT- SKEWNESS/OUTLIERS

E- EQUAL STANDARD DEVIATION- RESIDUAL PLOT DOES NOT SHOW CLEAR SIDEWAYS (CHRISSTMAS TREE PATTERNS)- just cap your way though this

R= random sample/experiement

C (conclude)

get degrees of freedom in there somewhere

• NAME IS ONE SAMPLE T INTERVAL)

degrees of freedom i

n-2

what distribution do you use for this

T distribution- use normal inv norm however remeber jsut do half the tails (tail probability_ (95% is .025

equation

point estimate (given slope0 ± (critical value) (standard error) (s is SD of residuals)

the width of a confidence interval is..

twice the margin of error- narrow confidence intervals are better- increasing sample size will decrease moe, or decrease confidence level

interpret confidence interval for the slope of a regression model

We are C% confident that the interval from _____ to ______ captures the slope of the population regression line (in context)

ex: We are 95% confident that the interval from -.55 to 16.13 captures the slope of the population regression line for predicting wait time until the next eruption (in minues) from the durates of the previous erpution (in minutes) for all Old faithful geyser eruptions in July 2019

Interpreting confidence level

In repeated random sampling with the same sample size, approximately c% of C% confidence interval crated will captured the slope of the population regression line.

ex: If we take many random samples of size 25 from the population of Old faithful eruoptions in july 2019, and use each sample to contruct a 95% confidence interval for the slope of the population regression line for predicting waittime unitl the next erpution (in minutes) from the duration of the previous eruption (in minutes), about 95% of those intervals would capture the trye slope

justifying a claim

• similar (contains 0 as a plausbile value, not CE)

Because of the confidence interval (-.55 to 16.13) contains 0 as a plausible value of the slope of the popualtion. regression line, there is not convincing evidence that the waittime until the next eruption of old faithful is linearly related to the duration of the previous eruption in july 2019- REMEMBER EVERYTHING IS FOR POPULATION

JUSTIFYING A CLAIM CONFDIENCE INTERVAL

does confidence interval include the claim of whoever-

matched pair t test vs linear regression interval test

linear regression uses one variable to predict the other, matched pair t test is interesed in mean difference

can you tell whether data is independent on a residual plot

NO- just if it’s linear or not

Slope is per

unit change of explanatory variable

conditions for signficance test for linear regression equation

L- LINEAR RELATIONSHIP- dufs the scatter plot and look at residual plot to describe

I- INDEPENDENT- 10% CONDITION

N- NORMAL- LOOK AT DOTPLOT- SKEWNESS/OUTLIERS

E- EQUAL STANDARD DEVIATION- RESIDUAL PLOT DOES NOT SHOW CLEAR SIDEWAYS (CHRISSTMAS TREE PATTERNS)- just cap your way though this

R= random sample/experiement

C (conclude)-

df of linear regression

N-2

(sample size)-2