develop a simple linear regression equation excel ph stat

0.95 in the equation is the slope of the linear regression, which defines how much of the variable is the dependent variable on the independent variable.

1.5 is the intercept which can be defined as the value which remains constant irrespective of the changes in the independent variable.

x here is an independent variable, and y is the dependent variable which changes with the change in the value of x by a certain value.

So the regression line can be defined as Y = a +bX which is Y = 1.5 + 0.95 * X One may choose to use one test over the other depending on context, but a t ratio is typically used for regression tests.įor more information about the linear regression, we can click the red triangle next to “Linear Fit” under the graph.A (Intercept) is calculated using the formula given belowĪ = (((Σy) * (Σx 2)) – ((Σx) * (Σxy))) / n * (Σx 2) – (Σx) 2 In simple linear regression, these two values will match because they are testing the same thing.

They two tests are different in that the parameter estimates uses a t test to form a t ratio, and the ANOVA partions the SStotal into SSregression and SSerror.

This p-value is exactly the same as the one calculated in ANOVA.

We are given the estimate of the slope of 1.77, the estimated standard error of 0.15, a t ratio of 11.77 formed by dividing the estimated slop by dividing the slope by the standard error, and a p-value of 0.0003 calculated from the t distribution. The standard error for intercept is substantially smaller because the formula for intercept has many more terms which could have the potential for more things to go wrong. we are also given the hours (slope) that is adding 1.77 hours for the grade that is expected. We are given the intercept estimate of where the line hits the y axis and we are given our t ratio and a p-value that is received from our appropriate t distribution.

(Actual sample estimate - Expected H 0)/ (Standard Error) The Parameter Estimates output gives these statistics in the form of t statistics.

Develop a simple linear regression equation excel ph stat