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Why did the coefficient of determination change when more variables were added to the model?
In regression with multiple independent variables, the coefficient tells you how much the dependent variable is expected to increase when that independent variable increases by one, holding all the other independent variables constant. Remember to keep in mind the units which your variables are measured in.
Why do estimated coefficients change in multiple regression?
If there are other predictor variables, all coefficients will be changed. The T-statistic will change, if for no other reason than the joint variance of the dependent variable Y is now different. All the coefficients are jointly estimated, so every new variable changes all the other coefficients already in the model.
Is the standard error of the temp coefficient statistical significance?
In fact, the standard error of the Temp coefficient is about the same as the value of the coefficient itself, so the t-value of -1.03 is too small to declare statistical significance. The resulting p-value is much greater than common levels of α, so that you cannot conclude this coefficient differs from zero.
When to look for significance without a p-value?
So most likely what your professor is doing, is looking to see if the coefficient estimate is at least two standard errors away from 0 (or in other words looking to see if the standard error is small relative to the coefficient value). This is how you can eyeball significance without a p-value.
When does a coefficient have a statistical significance?
A coefficient is significant if it is non-zero. The typical rule of thumb, is that you go about two standard deviations above and below the estimate to get a 95% confidence interval for a coefficient estimate.
What does a lower p-value in statistics mean?
A lower p -value is sometimes interpreted as meaning there is a stronger relationship between two variables. However, statistical significance means that it is unlikely that the null hypothesis is true (less than 5%).