Learn Simple Regression

Click on the graph to create data

Line Confidence Interval

Create a data set with two properties:

(i) You can draw a horizontal line inside the 99% line confidence interval.

(ii) You cannot draw a horizontal line inside the 95% line confidence interval.
ANSWER: Denoted by two asterisks after the slope t-stat, statistical significance at a 95% level means two things:

1. You cannot draw a horizontal line inside the 95% confidence interval. In other words, you reject the hypothesis that the line is flat (no relationship between X and Y) at a 95% level of confidence (5% Type I error).

2. You can draw a horizontal line inside the 99% confidence interval. In other words, you cannot reject the hypothesis that the line is flat at a 99% level of confidence (1% Type I error).

Slope t-statistic

Create a data set so that the slope t-statistic has one asterix after it.

Can you draw a flat line inside the 90% or 95% line confidence intervals?
ANSWER: A line is statistically significant at the 90% level if you can reject the null hypothesis that the line is flat. With one asterix after the t-stat, the line is statistically significant at a 90% level because the confidence interval does not include a flat line. It is not significant at the 95% level because you can draw a flat line inside the 95% confidence interval.

One-tail Hypothesis Test

Make sure the "One Tail" box is checked and create a data set with two properties:

(i) You cannot draw a negatively sloped line inside the 95% confidence interval.

(ii) You can draw a negatively sloped line inside the 99% confidence interval.

How many asterixis after the t-stat?
ANSWER: A line is positive (negative) and statistically significant if you can reject the null hypothesis that the line is negatively (positively) sloped. Denoted by two asterixis after the t-stat, a line is statistically significant at a 95% level because the line confidence interval does not include a negatively (positively) sloped line. It is not significant at the 99% level because the line confidence interval does include a negatively (positively) sloped line.

Point Confidence Interval

Uncheck the boxes denoting "line" confidence interval Make sure that the 95% confidence level and "Two-tail" boxes are checked.

(i) Create a data set with exactly 1 data point outside the 95% point confidence interval.
ANSWER: An "outlier" far from the regression line decreases the precision with which points are predicted by the regression line. This is reflected in a larger point confidence interval.

Trial and Standard Error: Learn Simple Regression

Simple
Regression

Differences
Between
Groups

Functional
Forms

Reverse Regression x=a+b*y

Confidence Interval

Line Point

Two Tail

One Tail

99%***

95%**

90%*

Residuals

Show

Plot

	Intercept	Slope
Value:
Std. Error:
t-Statistic:


Correlation:
R-Squared:
Observations:

© 2023 Luke M. Froeb, Keyuan Jiang & Gray Curtis