"did the intercept significance give us any inference about the relationship between variables?" - No.

@Rimatas:

Your first two sentences are correct. For the rest I have some concerns...

"If it is not significant then it is not worth including into equation." - I don't subscribe here. The intercept may be important in the model, independent of its statistical significance.

"However since the slope is also insignificant then in simple linear regression [...] slope does not really tell anything about the relationship between x and y" (bold by me) - If you remove the intercept term form the model then the estimate for the slope will change (and may become statistically significant). Further, you always have an estimate of the slope, be it significant or not. And the slope term does tell you something about the relation between x and y, no matter what the significance is. A slope close to zero just tells you that the expected change of y by one unit change of x is small. It may be that the precision of this estimate is too bad to distinguish a relevant from an irrelevant relation, but this is not neccesarily linked to statistical signifcance.

your data may be independent of X. if constant is significant and slope is not significant means, your data (y) may be || to x-axis if linear regression is assumed. 

As others have written the intercept is the mean of the response when all predictors are zero. You may wish to test that is this estimate is different from a specific hypothesized value and this does not have to be zero. It has much to do with your theory and expectations. Naively taking the estimate and dividing it by is standard error will allow you to evaluate if the estimate is significantly different from zero which may or may not be a sensible thing to do.   

You can radically change the intercept estimate by re-scaling the X variable say by centering that is  subtracting its  grand mean (xi - xbar)- this  will not change the slope term in a standard regression model. 

There are times when you want to force the intercept to be effectively zero - this is known as regression through the origin = so that when X is 0, Y is forced to be 0. This can be a suitable procedure when Y is the gold standard of measurement and X is an easier way to measure the same thing - you know from theory when X=0 so does Y. You can do this by omitting the intercept term in the model - software will have a command such as NOINTERCEPT.

The answer is NO

Kelvyn is correct, when the slope is not significant, the predicted value of  each x  is just the mean of y, in other words  the intercept being significant (and slope is not) is the same as saying  the mean of y is significantly different from 0.

Dear Rimantas,

although your answer is simple, it is wrong. Just having non-significance is no information to guide a sensible decision about whether or not keeping a coefficient in a model (as well as just having significance is no sensible guide to keep a coefficient in a model). There is no way to make sensible decisions just and only based on statistics. One needs a judgement call of the effects and the precisions one considered relevant for the purpose. This is substantial science and not statistics. Based on such judgements one can set up a procedure to conduct an experiment, then to calculate some statistics, and finally base one's decision on the value of this statistic. Without having made such judgements any calculated statistic is a hollow, uninterpretable value in outer space, since the frame for a judgement of such values is missing.

Of course no, the intercept is important to estimation or prediction of dependent variable.

The is definitely No

Dear All;

In my case I am using the non-linear regression with more 12 independent variables. I believe that incorporating the intercept is very important and there is no agreement on how to explain as it completely depends on the data at hand, My financial time series data come from different stock/bond markets and once I estimated the non- linear model I got highly significant intercept and also its coefficient is the highest among all other coefficients in the model, although it is clearly that I have some specific independent  variables significant across all the data set. (equity markets) in my sample, I tried to drop the intercept and most of those significant iv variables stay significant. with all of that I am still confused, not only that some published related studies found the same with similar data but have not commented on that on their paper. the t value for the intercept is high (between 12 o 35) depending on the equity market I am running the regression on. similar studies also transformed the data using fisher transform and other standardized. could anybody please advice here. 

Dear Abdelrazzaq

The mean of intercept is the value of dependent variable when the independent variable equal zero , all conclusion concerned on significance of regression coefficient , but we discuss about the significance of intercept in the analysis .

Best Regards

dear Khalid;

yes, this is what I am asking about, the high significance level of my intercept. ? 

No of course, the intercept is needed for a valued judgement or estimation

@ Helen

The discussion about the null hypothesis we going to test for intercept, and what the interpretation of significant intercept

regards

Hi, in a classical and simple linear model I think that a significant slope might mean a significant difference between starting values (no treatment applied).

Then if the slope is significant too this means that the treatment works.

i hope it helps

Hi all of you, would any one like to share his or her experience regarding the calibration curve and the best fit line model. My question is about the intercept and slope values of curve. Higher slope value are good predictors of the significance of curve and what about the intercept value, either higher or lower intercept values are good predictor, i mean good calibration curve.

Will it mean there is significant bias in the model? Others may answer on that. In a bivariate linear regression model, a non-significant slope will mean Y is not different from X. But I will do further tests to come to a conclusion.

Nayeema Ahmed : " a non-significant slope will mean Y is not different from X " - that interpretation is wrong (in several ways). If the slope is "non-significant" (when testing the hypothesis that the "true" slope is zero) the data is deemed insufficient to conclude wehther the "true" slope is positive or negative. A non-significant result by itself does neither rule out that the "true" slope can be considerably different from zero, nor that it is zero.

In a staight-line model the slope can not generally equal X, as X varies but in a straight line the slope is constant. If the slope would equal x, the function would be a parabola of the form 0.5x². If you meant "0" instead of "X", it follows what I wrote above.

The application of slope intercept in data analysis is to evaluate optimization.

The slope intercept (often labeled the constant) is the expected mean value (here expected mean is equal to the first derivative = a good situation for discriminant analysis ) of output Y when all X=0. (You may think it finding roots of the equation or extreme values when X is stationary or in the state of equilibrium).

If X never equals 0 (this means no equilibrium, or no stationary state or ), then the intercept has no intrinsic meaning.

Moreover, an insignificant regression coefficient means that the independent variable has no effect on the dependent variable, that is, its effect is statistically equal to zero.

Dear all

in generally the econometricians say that the interpretation of the slop parameter is more important than intercept parameter, it' OK but how do we explain when the intercept parameter is not statistically significant ?

Slimani Mohamed It all depend on context of what I am modelling and in what units stuff has been measured and the specification of the model; there is no universal rule. For example, if I am doing a logit analysis, an intercept of zero representing a probability of success of 50% for the reference category, which may be quite reasonable; in other situations it would be a sign that something has gone wrong. It is vital to work out who or what the intercept (with all Xs equal to zero) represents. Indeed, I usually work quite hard at specifying the model so that the intercept is a 'representative' person. And of course that does not mean that the slope is any less important.

Hi all

in my data I got the slop is statistically significant but the intercept is not statistically significant so in this case, should I remove the intercept and put it equal to zero? and can I accept this model?

why would you want to remove the intercept, what is the purpose ofdoing this? Is a value of zero expected; is it reasonable?

Wala Draidi I also observe the same. How it should be reported, please guide. I think we should keep the intercept as it has some value.

By the way, what significance intercept mean (while looking to multiple linear regression)?