Calculate standard error of slope
Notice that the slope of the fit will be equal to 1/k and we expect the y-intercept to be zero. Therefore, s is the dependent variable and should be plotted on the y-axis. That makes F the independent value and it should be plotted on the x-axis. Let’s assume that since you control the force used, there is no error in this quantity. Because linear regression aims to minimize the total squared error in the vertical direction, it assumes that all of the error is in the y-variable. Hooke’s law states the F=-ks (let’s ignore the negative sign since it only tells us that the direction of F is opposite the direction of s). You systematically varied the force exerted on the spring (F) and measured the amount the spring stretched (s). Let’s say you did an experiment to measure the spring constant of a spring. The LINEST function performs linear regression calculations and is an array function, which means that it returns more than one value. To find these statistics, use the LINEST function instead. The equation for the fit can be displayed but the standard error of the slope and y-intercept are not give. The regression coefficient is often positive, indicating that blood pressure increases with age.In Excel, you can apply a line-of-best fit to any scatterplot. Consider a regression of blood pressure against age in middle aged men. Computer packages will often produce the intercept from a regression equation, with no warning that it may be totally meaningless.
![calculate standard error of slope calculate standard error of slope](http://faculty.cbu.ca/~erudiuk/IntroBook/sbgraph/regre~16.gif)
For instance, a regression line might be drawn relating the chronological age of some children to their bone age, and it might be a straight line between, say, the ages of 5 and 10 years, but to project it up to the age of 30 would clearly lead to error.
![calculate standard error of slope calculate standard error of slope](https://slideplayer.com/slide/7022355/24/images/26/Standard+Error+for+the+Slope.jpg)
To project the line at either end – to extrapolate – is always risky because the relationship between x and y may change or some kind of cut off point may exist. They show how one variable changes on average with another, and they can be used to find out what one variable is likely to be when we know the other – provided that we ask this question within the limits of the scatter diagram. Regression lines give us useful information about the data they are collected from. Calculation of the correlation coefficient However, it is hardly likely that eating ice cream protects from heart disease! It is simply that the mortality rate from heart disease is inversely related – and ice cream consumption positively related – to a third factor, namely environmental temperature.
![calculate standard error of slope calculate standard error of slope](http://cameron.econ.ucdavis.edu/excel/mregression3.gif)
As a further example, a plot of monthly deaths from heart disease against monthly sales of ice cream would show a negative association. However, if the intention is to make inferences about one variable from the other, the observations from which the inferences are to be made are usually put on the baseline. In such cases it often does not matter which scale is put on which axis of the scatter diagram. The yield of the one does not seem to be “dependent” on the other in the sense that, on average, the height of a child depends on his age. It is reasonable, for instance, to think of the height of children as dependent on age rather than the converse but consider a positive correlation between mean tar yield and nicotine yield of certain brands of cigarette.’ The nicotine liberated is unlikely to have its origin in the tar: both vary in parallel with some other factor or factors in the composition of the cigarettes. This confusion is a triumph of common sense over misleading terminology, because often each variable is dependent on some third variable, which may or may not be mentioned. The words “independent” and “dependent” could puzzle the beginner because it is sometimes not clear what is dependent on what.