I am in my 2nd year at university and I am currently doing an assignment for further research methods. I need to do a correlation and multiple regression on three variables. My predictor variables are conscientiousness and achievement, and my criterion variable is life satisfaction. I'm struggling a bit with this and I just have a few questions.
1. in my introduction, I found that students who have a high need achievement motivation had low satisfaction with life. So would my hypothesis be that I expect a negative correlation?
2. if my hypothesis is that I am expecting a negative correlation between achievement and life satisfaction, would my 5th hypothesis be that I expect achievement to be a negative predictor of life satisfaction?
3. What is the difference between a variable being a positive predictor or a negative one?
4. In my multiple regression, for achievement both the beta value and the t value are negative and the p value is .599 so its non significant. What does this mean in terms of my hypotheses and report?
5. If my hypothesis was that I predict that there will be a significant negative correlation between achievement and life satisfaction, and in the pearsons correlation it shows that there is a negative correlation but is non significant, would I write that it does not support my hypothesis?
I would be really grateful if these questions were answered
Thank you
Dear Hanaa,
Here is my take on your questions.
1) Yes, that is the correct hypothesis.
2) I guess so, if you expect negative correlation than achievement would be a negative predictor.
3) Postive predictors are the ones with positive regression coefficients in this case. It means that predictor and the independent variable change in the same direction (reducing achievement would mean that satisfaction would increase). Vice versa for negative predictors.
4) and 5) Since beta is negative, you are certain that achievment has negative impact on satisfaction in your sample. However, since the results are not significant you cannot confirm your hypothesis, the relationship between these variables is not significant on population levels. It could be an issue of sample size, or something else, but in both cases your hypothesis is not confirmed.
Hanaa,
I have a few general comments. You are not supposed to look at the data, then formulate the hypotheses. If you knew from first principles that satisfaction and achievement are negatively correlated, then you pose that as a hypothesis. However, if you did not suspect that such would be the case, than your null hypothesis is that satisfaction and achievement are unrelated, vs the alternative that satisfaction is related to achievement. Next, you should always plot scatter diagrams of your data before doing the modelling. It might be fun to plot a three-dimensional scatter plot of the three variables and rotate the plot in order to make sense of the data. The next comment is that the chance of obtaining a statistically significant result depends on the sample size and the strength of the underlying relationship(s). The stronger the relationship and the larger the sample, the better the probability that the regression relationship will be significant. There is also the possibility that the relationship is not linear (a straight line), but a curve. So, do some exploring of your data before you draw conclusions about the model.
When you do a multiple regression analysis your independent or predictors are conscientiousness and achievement,
and the variable you are to explain is life satisfaction = dependent variable. This is your model 1 (use enter for this model). Your ANOVA is there just to tell you if you can do a regression analysis or not. The thing that is important in a regression analysis is your R 2,
this squared R tells you how big each variable's variance is plus all shared variance together is in your model. Then if your R2 is e.g. ,451 you want to know how much your conscientiousness contributes to or explains life satisfaction. Then you look at your part correlation. Your squared part correlation tells you in % that conscientiousness explains e.g. 15% of life satisfaction. The you look at your achievement and find out that it explains about 10%. Nota bene
your part correlations do not add up to .451 because they do not include shared variance only unique variance for a certain variable explaining life satisfaction. I attach my examples:
Interpreting Output for Multiple Regression in SPSS
https://www.youtube.com/watch?v=WQeAsZxsXdQ
Conduct and Interpret a Multiple Linear Regression
What is Multiple Linear Regression?
Multiple linear regression is the most common form of the regression analysis. As a predictive analysis, multiple linear regression is used to describe data and to explain the relationship between one dependent variable and two or more independent variables.
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At the center of the multiple linear regression analysis lies the task of fitting a single line through a scatter plot. More specifically, the multiple linear regression fits a line through a multi-dimensional cloud of data points. The simplest form has one dependent and two independent variables. The general form of the multiple linear regression is defined as for i = 1…n.
Sometimes the dependent variable is also called endogenous variable, criterion variable, prognostic variable or regressand. The independent variables are also called exogenous variables, predictor variables or regressors.
Multiple Linear Regression Analysis consists of more than just fitting a linear line through a cloud of data points. It consists of three stages: 1) analyzing the correlation and directionality of the data, 2) estimating the model, i.e., fitting the line, and 3) evaluating the validity and usefulness of the model.
There are three major uses for Multiple Linear Regression Analysis: 1) causal analysis, 2) forecasting an effect, and 3) trend forecasting. Other than correlation analysis, which focuses on the strength of the relationship between two or more variables, regression analysis assumes a dependence or causal relationship between one or more independent and one dependent variable.
Firstly, it might be used to identify the strength of the effect that the independent variables have on a dependent variable. Typical questions would seek to determine the strength of relationship between dose and effect, sales and marketing spend, age and income.
Secondly, it can be used to forecast effects or impacts of changes. That is to say, multiple linear regression analysis helps us to understand how much the dependent variable will change when we change the independent variables. A typical question would be “How much additional Y do I get for one additional unit X?”
Thirdly, multiple linear regression analysis predicts trends and future values. The multiple linear regression analysis can be used to get point estimates. Typical questions might include, “What will the price for gold be six months from now? What is the total effort for a task X?”
The Multiple Linear Regression in SPSS
Our research question for the multiple linear regression is as follows:
Can we explain the reading score that a student achieved on the standardized test with the five aptitude tests?
First, we need to check whether there is a linear relationship between the independent variables and the dependent variable in our multiple linear regression model. To do so, we check the scatter plots. We could create five individual scatter plots using the Graphs/Chart Builder… Alternatively we can use the Matrix Scatter Plot in the menu Graphs/Legacy Dialogs/Scatter/Dot…
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The scatter plots indicate a good linear relationship between writing score and the aptitude tests 1 to 5, where there seems to be a positive relationship for aptitude test 1 and a negative linear relationship for aptitude tests 2 to 5.
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Secondly, we need to check for multivariate normality. This can either be done with an ‘eyeball’ test on the Q-Q-Plots or by using the 1-Sample K-S test to test the null hypothesis that the variable approximates a normal distribution. The K-S test is not significant for all variables, thus we can assume normality.
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Multiple linear regression is found in SPSS in Analyze/Regression/Linear…
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To answer our research question we need to enter the variable reading scores as the dependent variable in our multiple linear regression model and the aptitude test scores (1 to 5) as independent variables. We also select stepwise as the method. The default method for the multiple linear regression analysis is ‘Enter‘, which means that all variables are forced to be in the model. But since over-fitting is a concern of ours, we want only the variables in the model that explain additional variance. Stepwise means that the variables are entered into the regression model in the order of their explanatory power.
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In the field Options… we can define the criteria for stepwise inclusion in the model. We want to include variables in our multiple linear regression model that increase F by at least 0.05 and we want to exclude them again if the increase F by less than 0.1. This dialog box also allows us to manage missing values (e.g., replace them with the mean).
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The dialog Statistics… allows us to include additional statistics that we need to assess the validity of our linear regression analysis. Even though it is not a time series, we include Durbin-Watson to check for autocorrelation and we include the collinearity that will check for autocorrelation.
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In the dialog Plots…, we add the standardized residual plot (ZPRED on x-axis and ZRESID on y-axis), which allows us to eyeball homoscedasticity and normality of residuals.
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