Sara Bassichis STA2023 Mini Project July 13 2023 1 State the question Interference a What is the relationship between Islanders Age and how long they take to perform a Stroop Test 2 Present your data for the 60 individuals in an organized table 3 Make a scatterplot of the data and describe using the four characteristics direction outliers trend and strength a The graph s direction represents the positive association between the Islander s Age and their performance on the Stroop test The trend on the graph is clearly linear and the strength between the relationship of x Age and y Stroop Test Performance is very strong with minimal outliers apparent 4 Show the output from a statistical software package of the Least Squares Regression line of output State the least squares regression output This varies by software program but this must include the fitted line plot R squared and the equation a The least squares regression output is yST 664 9 3x 5 State and interpret the slope if applicable a The slope of the line can be found in front of the x value in the equation and is the measurement that assesses the strength of the relationship between the two variables Age x and the Stroop Test y The slope of the line for the date is 3 therefore showing that y Stroop Test increases on average for every one unit change in x Age In conclusion as Age increases the Stroop Test will increase by 3 6 State and interpret the y intercept if applicable a The y intercept is 664 9 however no data around x equals zero Therefore interpreting the y intercept would not make sense because the smallest data collected for x Age is 18 7 State and interpret the correlation coefficient R2 86 8 a To find the correlation coefficient we will divide R squared by 100 then take the square root to 0 868 86 8 100 0 868 0 9317 b A positive strong correlation because r is relatively close to 1 8 State and interpret R2 a The R squared is 0 868 meaning about 86 8 of the participants of this study had their performance on the Stroop Test explained by their age 9 For the first individual from whom you collected information find the predicted value of y using the least squares equation and then find the residual using the equation for the residual Show your work yST a bx yST 664 9 3 57 Predicted Value of yST 835 9 Residual Observed y Predicted y Residual 842 835 9 Residual 6 1 a The observed performance on the Stroop Test was 6 1 m s more than the predicted Stroop test score found with this equation 10 Answer the question Is there a relationship between Age and the time taken to perform a Stroop Test Interference Use the information found in the previous section to support your claim Use information about the statistical concepts that you learned in the regression module and in this project to justify your claim a Yes age and the time taken to perform a Stroop Test Interference are related as shown by the strong and positive linear relationship between the two variables At the correlation coefficient of 0 9317 it is a strong relationship Since the R squares is 0 868 most of the sample size s age affected their performance time on the Stroop Test The near 90 is significant information to further back up the conclusion of the clear correlation between these two variables 11 Extra Credit Is there a difference in the relationship between Age and the time taken to perform a Stroop Test Interference for males and females Run the regression model with only males and then with only females Do you see a change in R squared In slope You must include the output to receive credit a Is there a difference in the relationship between Age and time taken to perform a Stroop Test Interference for males and females b Female i Female Regression Line 670 8 2 840x ii y intercept 670 8 iii slope 2 840 iv R2 0 819 v R 0 9050 c Male i Male Regression Line 659 0 3 135x ii y intercept 659 0 iii slope 3 135 iv R2 0 911 v R 0 9545 d The difference in the relationship between Age and Time it took on the Stroop Test when separating the data by gender is fairly small Both graphs represent strong positive correlations between Age x and Stroop Test Performance y Females had a higher y intercept whereas males had a larger slope The R value for men is stronger than that of females Since both the slope and the R2 value are greater for males than females the conclusion can be drawn that Age plays a greater role in how much time males take on the Stroop test than how much time females take on the test