Analytics Tutor
Hypothesis testing, regression & demand analysis
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2.0
20.0
Sum of raw errors
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SSE (your line)
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OLS minimum SSE
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| Point | Actual Y | Predicted Ŷ | Residual | Residual² |
|---|
Drag the sliders to move the line. Watch the squares and table update. Notice the sum of raw errors stays near zero for many bad lines — that is why we square them. Hit "Snap to OLS" to see the minimum SSE.
Confidence Interval Calculator
Enter values and work through each step. Formula: CI = x̄ ± t* × (s / √n)
Excel: =T.INV.2T(α, n−1) for critical t | =CONFIDENCE.T(α, s, n) for margin of error directly
t-test Lab
Two scenarios, two different tests. Choosing the right T.TEST type — paired (type 1) vs. independent-samples Welch's (type 3) — is part of the lab. Same hypothesis testing logic you already know, applied to differences between groups.
Animate critical t
The t-distribution with rejection regions. Set alpha and df, then drag the test statistic to see when you reject H₀. Toggle between testing a mean and testing a regression coefficient — same distribution, same logic, different formula.
43
Critical t
±2.017
Your t-statistic
0.00
Decision
Fail to reject H₀
Formula: t = (x̄ − μ₀) / (s/√n) | Critical t from: =T.INV.2T(α, df) | If |t| > critical t → reject H₀
Verify the numbers
Use the Salary vs Experience output below to calculate the missing values. Type your answer and click Check — or use the Hint button if you are stuck. Every number in Excel output can be derived from the others.