What is the use of "t-test for an independent sample or student's t-test" in linear regression? when we are not going to use it to interpret our data like we don't compare groups in our data. How helpful is it for a simple linear regression in interpreting its table data?
I've searched that " A t-test for testing significance of regression coefficient is used to test the significance of regression coefficients in linear and multiple regression setups."
Can someone expound this?
@ Victoria
I suggest pl express your problem in an understandable way.
Although the problem is not clearly identified , I venture a blind shot and I hope that it helps. In using t- test for independent samples, you have an observed t value. Then, you compute the degree of freedom ( df= N-2) and refer to the t distribution table to calculate t critical values for alpha levels at 0.01 and 0.05. If the observed t value is equal to or larger than t critical values, you can safely reject the targeted null hypothesis.
Best of luck,
R. Biria
Dear Victoria,
In regression models, the significance of the coefficients is tested in order to verify which independent variables we should keep for the final model. So a hypothesis test is performed in the coefficients of the independent variables, where the null (H0) hypothesis states that the independent variable coefficient equals zero where the alternative hypothesis (H1) states that the coefficient is different to zero. So in regression we want to reject the null hypothesis (sig
In a regression analysis, you get estimates for the coefficients and standard errors of these estimates. Under the assumption that the response is normal distributed (conditional on the predictors), the ratio of an estimate and its standard error ("t-values") are t-distributed under H0 (with n-k degrees of freedom; n=sample size, k=number of coefficients). Thus, one can use the t-distribution to get the probability Pr(|t| > |tobserved|) (how likely we expect to get more extreme t-values than the one calculated from the observed data), what is the p-value of a t-test.
It is enlightning to see it from the opposite point-of-view: Think of data (Y) from two groups A and B, and you perform a standard t-test, testing H0: µA=µB. This problem can be formulated as a regression analysis. Instead of distinguishing two groups, you would understand the group-membership be given as a categorical predictor G that can take the two values A or B. This predictor can be expressed as a numerical variable X, that takes 0 when G=A and 1 when G=B (-> the group is 0/1 coded).
You now have a series of Y values and another, corresponding series of X values. So you can formulate a regression equation:
Y = b0 + b1*X
If a partictular Y value comes from group A, X would be 0 and the equation is actually Y = b0 + b1*0 = b0. Thus, the coefficient b0 is the (expected, mean) Y-value of a member of group A. It follows that b0 is the (expected, mean) difference between B and A.
You can plot the data like this in a scatterplot. The values from group A will all lie on the vertical axis at X=0, and the values from group B will all line up vertically at X=1. The regression line through these points will have an intercept at the mean of the "group A values" (=b0) and a slope that is just the mean difference between the group B and the group A values (=b1), because the line will go through the mean Y for the group B values and the horizontal distance is just 1.
So the test of the mean difference is equivalent to testing the coefficient b1 in the regression model.
Hi Victoria
If you run bivariate linear regression you will get exactly the same result as in a t-test (see the t-value in the regression output and compare with a t-test). The advantage with regression is that you can do a multivariate model, i.e., you can "control for" socio-demographic variables or set up a model with all the relevant independent variable you want to examine and see their relative influence on the dependent variable.
Best
John-Kåre
Our conceptual framework is this. We will use the simple linear regression to analyse our data. We used the Gender for our demographic profile of the respondents only not for inferential statistic such as t-test independent , it is only for descriptive statistics only for point of reference as we used Purposive sampling technique for our Data Gathering. I thank you for all of you professionals who responded to our concern. It is appreciated. May I request to explain the use of the "t-test in the coefficients" also the "ANOVA" when our participants where not in independent groups.
And to simply interpret our data, we will not going to use the multivariate to analyse our data. Thank you!!
Best,
Victoria
- Badges
- Science topic
- Similar topics
- Philosophy
- Esthetics
- Interpretation