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Introduction
Introduction
In Module 09, we have learned how to examine the correlation between variables using correlation analysis by jamovi. The directional effect, IV, or DV, are not specified in a correlational relationship. If we want to know the directional effect, such as the effect of the independent variable(s) on the dependent variable, we can also use linear regression to find out the relationship between variables.
Linear regression is a predictive analysis to model the relationship between the independent variable(s) and dependent variable. It helps us identify how good each predictor variable (independent variable) is in predicting an outcome (dependent variable).
1. What is linear regression?
1. What is linear regression?
In a simple linear regression model, the slope and the intercept explain the relationship between one independent variable and one dependent variable. The regression equation for simple linear regression is defined by the formula:
y = m(x) + c
where y = estimated dependent variable, m = slope, x = independent variable, c = intercept.
The slope (m) represents how much the dependent variable y changes if the independent variable x increases by one unit. For example, suppose the slope (m) equals -0.3 in a simple linear regression with the number of apples a person eats per week as the predictor (x) and the number of visits to the doctor per year as the outcome (y). This means, on average, if a person eats one more apple per week, he/she is estimated to pay 0.3 visits less to the doctor per year.
The intercept (c) represents the estimated value of the dependent variable y when the independence variable x equals 0. In the example above, if the intercept is 4, it means that a person who eats zero apples per week is estimated to visit a doctor 4 times a year.
2. Example 1: linear regression of "SNS" and "BSC"
2. Example 1: linear regression of "SNS" and "BSC"
Aside from correlation, we also want to know how good can self-control predict the time people spend on social media. So we need to use the linear regression model to test the prediction.
Q: How do we test the prediction of "BSC" on “SNS”?
A: We use the “Linear Regression” under “Regression” in jamovi.
Example 9.2_Regression_SNS_BSC.mp4
Regression model equation:
Estimated (SNS) = 4.99 - 1.10 (BSC)
Conclusion/ Interpretation (APA format):
The results of the linear regression indicated the predictor explained 22.6% of the variance (R2 = .226, F(1, 198) = 58.0, p < .001). It was found that self control significantly predicted the hours people spent on social media (β = -1.10, p < .001).
3. Example 2: linear regression of "PerAttract" and "NumRel"
3. Example 2: linear regression of "PerAttract" and "NumRel"
We can also apply linear regression model on predicting the number of romantic relationships. There may be more predictor variables, but we only look at the perception of attractiveness here in this example. To find out how good can the perceived attractiveness predict the number of relationships, we can use linear regression.
Q: How do we test the prediction of “PerAttract” on “NumRel"?
A: We use the “Linear Regression” under “Regression” in jamovi.
Example 9.4_Regression_PerAttract_NumRel.mp4
Regression model equation:
Estimated (NumRel) = -0.3185 + 0.0289 (PerAttract)
Conclusion/ Interpretation (APA format):
The results of the linear regression indicated the predictor explained 50.1% of the variance (R2 = .501, F(1, 198) = 198, p < .001). It was found that PerAttract significantly predicted the number of romantic relationships (β = .0289, p < .001).
Interpretation of coefficients: If a person rates himself/herself as one point more attractive, he/she is estimated to have 0.0289 more relationships. If a person rates himself/herself as zero points in the perceived attractiveness, he/she is estimated to have -0.3185 times of relationships (?!).
Note that the intercept interpretation may not be very meaningful, but it could be of help if "x = 0" is a meaningful value.
4. Effect size interpretation
4. Effect size interpretation
Same as other statistical tests, we can measure the effect size in a regression analysis. Actually, the effect size for the regression analysis is the r2 in the main analysis. We measure the magnitude of effect by calculating the proportion of the variance in the dependent variable that can be explained by the predictor(s). Theoretically, the range of r2 is from zero to one (0 - 1). E.g., if r2 = .13, it means that 13% the variance in the DV can be explained by the predictor(s), and 87% of the variance in the DV is attributed to other factors that are not related to the predictor(s).
Module Exercise
Module Exercise
Complete the exercise!
Complete the exercise!
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