Student Correlation and Simple Linear Regression(1) (1)

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Feb 20, 2024

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1Correlations Data Set: PETOTAL Bivariate correlations ► one variable is correlated with another variable, that is, one pair of variables at a time. We will be using Pearson Product-Moment Correlation Coefficient formula under Analysis ► Correlation If the correlation coefficient ( r) is positive , as one variable increases, the other variable also increases or one variable decreases, the other variable also decrease. If the r is negative , as one variable increases, the other variable decreases. The strength of the relationship is indicated by the magnitude of the number, not the sign. Which is stronger correlation r (150) = -.89, p = .02 or r (150) = .75, p =.02 Casewise vs Pairwise deletion: By default, JASP (R) uses pairwise MD deletion. The correlation output is based on the available pairs of variables. The N reflects the number of cases for the pairs of variables only, regardless of the number of scores for the test. Some programs use casewise MD deletion. This means that whey you select a list of variable, the output will include only those cases which have no missing data on any of the variables listed. If some cases have some missing data on any of the variables, these cases will automatically be excluded when calculating the correlation coefficients.

Question: Describe the relationship between participant’s self-control scale/general resourcefulness (SCST) and the following variables: C_MOT, STRESS, ADJUST and AVGDRINK. Bivariate Correlation – Continuous variables- use Pearson’s r Open JASP --- 3 lines--- Open --- Browse Computer ----find H drive ---- PETOTAL  Go to top tool bar ----select Regression -----Correlation  Select SCST, C_MOT, STRESS, ADJUST and AVGDRINK move to the variable box  Click on: o Sample Correlation Coefficient ----Pearson’s r o Alt. Hypothesis ---- Correlated o Additional Options  Report Significance  Confidence Intervals  Sample Size  If you wish you can do a Scatter plots o Options  Exclude cases pairwise Correlation Matrix Output

Pearson's Correlations Variable SCST C_MOT STRES S ADJUSTAVGDRINK 1. SCST n — Pearson's r — p-value — Upper 95% CI — Lower 95% CI — 2. C_MOT n 161 — Pearson's r -0.242 — p-value 0.002 — Upper 95% CI -0.090 — Lower 95% CI -0.382 — 3. STRESS n 161 161 — Pearson's r 0.022 0.027 — p-value 0.785 0.731 — Upper 95% CI 0.176 0.181 — Lower 95% CI -0.133 -0.128 — 4. ADJUST n 161 161 161 — Pearson's r 0.364 -0.195 -0.034 — p-value 2.058×10 -6 0.013 0.673 — Upper 95% CI 0.491 -0.041 0.122 — Lower 95% CI 0.222 -0.339 -0.187 — 5. AVGDRINK n 161 161 161 161 — Pearson's r -0.118 0.321 0.212 0.002 — p-value 0.135 3.300×10 -5 0.007 0.979 — Upper 95% CI 0.037 0.453 0.355 0.157 — Lower 95% CI -0.268 0.175 0.059 -0.153 —

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Interpreting these correlations: Remember df for Pearson correlation is N-2 1. SCST and C_MOT - significant negative correlation - r (159) = -.24, p = .002, 95% CI[ -.38, -.09] - as general resourcefulness increases the reasons for using coping motivation appears to decrease. - we are 95% confident that the population correlation falls between -0.38 and -0.09 2. SCST and STRESS - Report the correlation statistic and meaning. 3. SCST and ADJUST – explain Scientific notation 2.058 x 10 -6 = .000002058 - Report the correlation statistic and meaning. 4. SCST and AVGDRINK - Report the correlation statistic and meaning.

Regression (Prediction) Data Set: PETOTALgroup Whenever there is a significant relationship between two variables, you can predict one from the other. The stronger the relationship, the more accurate the prediction.  Open up new data set PETOTALgroup in JASP  Check to make sure the variables are listed as the correct type (scale, nominal, ordinal)  In the top tool bar select Regression-----Correlation o Select ATTITUDE and AVGDRINK and move to the variable box o Sample Correlation ----select Pearson’s r o Alt. Hypothesis ---Correlated o Additional Options-----Display pairwise, report significance, confidence intervials, sample size o Plots---Scatter Plots o Missing Values ---Exclude cases pairwise What is the relationship between average number of drinks consumed at a party or social gathering (AVGDRINK) and ones personal attitude toward the consumption of alcohol abuse survey (ATTITUDE; the higher the score the liberal ones attitude)?

Output Pearson's Correlations Variable ATTITUDEAVGDRINK 1. ATTITUDE n — Pearson's r — p-value — Upper 95% CI — Lower 95% CI — 2. AVGDRINK n 157 — Pearson's r 0.537 — p-value 4.153×10 -13 — Upper 95% CI 0.640 — Lower 95% CI 0.415 — What is the correlation between the average number of drinks and alcohol attitude? Statistics ? Meaning? The 95% CI? What does it mean? What is the 95% confidence interval of this relationship?

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Scatter plot X – predictor ATTITUDE Y – outcome AVGDRINK Smoothing - Select -lm – linear model Run  Decide which variable is X (predictor) and which one is Y (dependent/outcome/being predicted).  Alcohol attitude predictor  Average drink is the dependent  Go to JASP----Regression If a person’s average alcohol attitude score (ATTITUDE) is 9 how many drinks (AVGDRINK) do they consume on average at a party or social gathering?

 Select AVGDRINK for the Dependent Variable box  Select the Predictor (ATTITUDE) for the Covariates box  Statitistics---- o Estimate o Model fit o Residuals---- Statistics Output Model Summary - AVGDRINK Mode l R R² Adjusted R²RMSE H ₀ 0.000 0.000 0.000 2.869 H ₁ 0.537 0.288 0.284 2.428 Coefficients Model Unstandardize d Standard ErrorStandardized t p H ₀ (Intercept) 4.045 0.229 17.66 7 4.652×10 -39 H ₁ (Intercept) -0.419 0.596 -0.704 0.483 ATTITUDE 0.434 0.055 0.537 7.926 4.153×10 -13 Residuals Statistics MinimumMaximum Mean SD N Predicted Value -0.419 8.270 4.045 1.540 157 Residual -5.663 10.205 -1.575×10 -19 2.420 157 Std. Predicted Value -2.898 2.743 -2.399×10 -16 1.000 157 Std. Residual -2.349 4.221 3.577×10 -4 1.003 157 Y′ = b(X) + c  Fill in the formula with the slope, constant and predictor value  Y’ =  How many drinks is predicted if the person has an alcohol attitude score of 9?

 Again, the stronger the relationship, the greater the accuracy.  What is the Residual standard error?  The accuracy of a prediction is? Note. This does not represent the .95CI  The coefficient of determination is?  What does it mean? How accurate is the prediction? What is the coefficient of determination or effect size

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Student Correlation and Simple Linear Regression(1) (1)

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