Stats.Blue

# Simple Linear Regression Calculator

 Variable Names (optional): Explanatory (x) Response (y) Data goes here (enter numbers in columns): Include Regression Line: Include Regression Inference: Null Hypothesis: $H_0: \beta=0$ Alternative Hypothesis: $H_a: \beta$ $\neq$ $<$ $>$ $0$ Significance level: $\alpha=$ 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005

• Values of the response variable $y$ vary according to a normal distribution with standard deviation $\sigma$ for any value of the explanatory variable $x$. The quantity $\sigma$ is an unknown parameter.

• Repeated values of $y$ are independent of one another.

• The relationship between the mean response of $y$ (denoted as $\mu_y$) and explanatory variable $x$ is a straight line given by $\mu_y=\alpha+\beta x$ where $\alpha$ and $\beta$ are unknown parameters.

Display output to

 Regression Line: Correlation: R-squared:
 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% for $\mu_y$ at $x=$: 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% for $y$ at $x=$:

Residual Plot
 Residuals $y-\hat{y}$
Regression Inference: $y=\alpha+\beta x$
 Degrees of Freedom: $df=n-2=$ Estimate of Slope: Standard Error Slope: Regression Standard Error: $t$-Statistic: % Confidence Interval for $\beta$: $p$-value: $p=$