Help with Regression Interpretation

#1
Hi -
Thanks in advance for any help or advice on this! I know very little about statistics, but I have performed a multiple regression analysis in Minitab, and have my results in front of me. The problem is, I am not certain on what I am looking at. A statistics primer that I read says that if the p value is less than .3 but greater than 0, then there is a weak correlation, if it is greater than .3 but less than .7 then there is a moderate correlation, and if it is greater than .7 then there is a strong correlation. Given that information (if it is even correct), would I be right in saying that the below results are telling me that there is a moderate correlation for each of the variables, with the exception of variable #2, which shows a very strong correlation?

Predictor Coef SE Coef T P
Constant 42.75 12.68 3.37 0.002
1 -0.2026 0.1966 -1.03 0.310
2 0.0118 0.2233 0.05 0.958
3 0.1259 0.2344 0.54 0.595
4 0.1969 0.2669 0.74 0.466

Also, what exactly is the ANOVA telling me?

Analysis of Variance

Source DF SS MS F P
Regression 4 599.0 149.7 0.37 0.828
Residual Error 33 13348.4 404.5
Total 37 13947.4

Again, I appreciate any help on this. Thanks a bunch!:)
 

Dragan

Super Moderator
#2
Hi -
Thanks in advance for any help or advice on this! I know very little about statistics, but I have performed a multiple regression analysis in Minitab, and have my results in front of me. The problem is, I am not certain on what I am looking at. A statistics primer that I read says that if the p value is less than .3 but greater than 0, then there is a weak correlation, if it is greater than .3 but less than .7 then there is a moderate correlation, and if it is greater than .7 then there is a strong correlation. Given that information (if it is even correct), would I be right in saying that the below results are telling me that there is a moderate correlation for each of the variables, with the exception of variable #2, which shows a very strong correlation?

Predictor Coef SE Coef T P
Constant 42.75 12.68 3.37 0.002
1 -0.2026 0.1966 -1.03 0.310
2 0.0118 0.2233 0.05 0.958
3 0.1259 0.2344 0.54 0.595
4 0.1969 0.2669 0.74 0.466

Also, what exactly is the ANOVA telling me?

Analysis of Variance

Source DF SS MS F P
Regression 4 599.0 149.7 0.37 0.828
Residual Error 33 13348.4 404.5
Total 37 13947.4

Again, I appreciate any help on this. Thanks a bunch!:)

Really? Based on what evidence above do you have to demonstrate that; "variable #2, shows a very strong correlation" ?
 
#3
Hi,

I don’t know whether you know hypothesis testing or not. If you don’t have idea about hypothesis testing please first refer the link http://en.wikipedia.org/wiki/Statistical_hypothesis_testing . Then read the following lines.

Let me first give you the interpretation of Anova result.
In Anova, Null Hypothesis is all coefficients other than intercept are zero and alternate Hypothesis is at least one coefficient other than intercept is non zero. p value plays a significant role in accepting or rejecting null hypothesis. One often rejects a null hypothesis if the p-value is less than 0.05 or 0.01 for 95% & 99% confidence limit respectively.

So in Anova you are getting p value for regression is 0.828.That means we are failing reject the null hypothesis that all coefficients other than intercept is zero. So for this data anova result is implying that other than constant term no other variable is playing role in determining the outcome. Still now we don’t have any idea whether constant term is playing a role in determining the outcome or not.

Now, let’s analyze the result of Regression. For regression null hypothesis for all bi is bi=0 and alternate hypothesis is bi<>0.Where b0 is constant term and all other bi (for i<>0) are coefficient of ith variable.

Now here you are getting p value for constant only is less than 0.05.Then with 95% confidence limit we can conclude that only constant term in your equation is playing role to determining outcome variable.
Means instead of y= b0 + b1x1+ b2x2+ b3x3 ….. your regression equation will be
y= b0
For your problem b0 is 42.75.