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### Course: AP®︎/College Statistics>Unit 13

Lesson 1: Confidence intervals for the slope of a regression model

# Confidence interval for the slope of a regression line

Confidence interval for the slope of a regression line.

## Want to join the conversation?

• How is SE coef for caffeine found? We just input data from one sample of size 20 into a computer, and a computer figure out a least-squares regression line. That is we get an output of one particular equation with specific values for slope and y intercept. But how can a computer figure out (or estimate) standar error of slope if he get data from just one sample? Shouldnt we have at least a few samples, and then measure tha variance of slope coefficient for different samples, and only then estimate the tru variance for samplin distribution of slope coefficient?
• The formulas for the SE of coef for caffeine doesn't seem to need multiple different samples, with multiple different least-squares regression slopes.

The formulas can be found here:
• How do you find t with a calculator??
• Using a graphing calculator such as the TI-84, usually a command called "invT" will help you find it. In the TI-84, you can access invT using this set of commands:

2nd VARS
4: invT(

Here you can enter the area and df values to calculate for the t value. Note that you should enter the area of the "tail probability p" from the t value chart NOT the confidence level. (Ex: entering .025 instead of .95)
• why degree of freedom is "sample size" minus 2?
• "Degrees of freedom for regression coefficients are calculated using the ANOVA table where degrees of freedom are n-(k+1), where k is the number of independant variables. So for a simple regression analysis one independant variable k=1 and degrees of freedeom are n-2, n-(1+1)."

Credit: Monito from Analyst Forum.
• Why don't we divide the SE by sq.root of n (sample size) for the slope, like we do when calculating the confidence interval on the the mean of a sample (mean +- t* x SD/sq.root(n))?
• Whats the relationship between SE and S?
(1 vote)
• How would I find t* using the TI calculator in this problem?
(1 vote)
• Using the TI-84, a command called "invT" will help you find t*. In the TI-84, you can access invT using this set of commands:

2nd VARS
4: invT(

Here you can enter the area and df values to calculate for the t value. Note that you should enter the area of the "tail probability p" from the t value chart NOT the confidence level. (Ex: entering .025 instead of .95)
(1 vote)
• Again, i think that Caffeine should have been the Dependent Variable & hence on the y axis.