The corrections need to be only on #2, 12, and 17. I have an existing order #40034
Chapter 7 Comprehensive Questions Liberty University Gwynnedolynne James May 4, 2019 Solution 2: Physical Attractiveness Positivity of Facial Expression Negative emotion .04 (x1) -.27 (x4) Nurturance -.06 (x2) .22 (x5) Well Being .03 (x3) .27 (x6) a. The values in the table determines the Pearson correlation or r between the respective variables. If r is the correlation, r2 represents the probability that there could be a causal relationship between two variables (x1)2 = 0.0016 (x2)2 = 0.0036 (x3)2 = 0.0009 (x4)2 = 0.0729 (x5)2 = 0.0484 (x6)2 = 0.0729 At alpha/2 = 0.05/2 = 0.025 (two tailed test), significance level the value of r2 less than 0.025 that there is statistically significant correlation between two variables. b. Based on this, the significant variables to determine the state at age 52 (dependent variable) from college photos, parameters, (independent variable) are physical attractiveness for negative emotionally, nurturance, and wellbeing, other three correlations are rejected to determine causal relationship. c. It is known that the correlation between two variables does not imply causation. Thus, causal relation between two variables cannot be concluded based on this study. d. It would not be appropriate to generalize these findings to the men as the results relates to the study for female only. e. The scatter plot would have provided the visual interpretation and the nature of the relationship between these variables based on scatter plot we can make whether a linear or non-linear relationship exist between these variables. Solution 3: Correlation does not imply Causation. Correlation between two variables does not imply that one variable causes the other variable. Correlation coefficient provides the strength and direction of relationship between two variables suggested by the data. However, if there is a natural causal relationship between the variables, then correlation can be interpreted as evidence for a causal relationship between two variables. For example, height and weight of a group of persons, or income and expenditure of a group of families. 1 2 3 4 5 6 7 Robin Henson @ 2019-05-05T21:13:09-07:00 this is not what r2 tells us Robin Henson @ 2019-05-05T21:14:12-07:00 not clear which, if any, correlations (r) you are saying are stat sig, which is what the question is asking. Robin Henson @ 2019-05-05T21:15:01-07:00 not cleare what you are saying here, but need to state clearly what correlations are stat sig, if any, after invoking the alpha correction. Robin Henson @ 2019-05-05T21:16:13-07:00 incorrect. Robin Henson @ 2019-05-05T21:16:41-07:00 true, so why are you saying causal things above? Robin Henson @ 2019-05-05T21:17:20-07:00 other things? outliers? homoscedasticity? Robin Henson @ 2019-05-05T21:18:22-07:00 good, or when there are well controlled experimental designs, but that is a matter of research design, not statistical analysis. Solution 4: Since X and Y have a correlation of –0.64, it signifies that one unit change in X will display a -0.64 unit change in Y. Thus, 1-sd change in X will imply -0.64*1-sd change in Y = 0.64 SD change in zY. Solution 5: Correlation of determination signifies the percentage of variance in Y that can be predicted from X. Thus, Coefficient of determination = r² = 0.50 Correlation Coefficient = r = sqrt(50) = 0.7071 Thus, the correlation between blood pressure and HR is 0.7071. Solution 6: Using the Bonferroni procedure, the PCα used to test the significance of each individual r value is set at EWα / k . EWα = 0.05 k = 4 Thus, PCα = 0.05/ 4 = 0.0125 Thus, required value of PCα = 0.0125 Solution 9: The value of r (correlation coefficient) signifies the strength and direction of the linear relationship between two variables. It is always between -1 and +1, inclusive. An r of –1 signifies a perfect negative correlation, whereas an r of +1 signifies a perfect positive correlation between the variables. The value of r2 (coefficient of determination) signifies the percentage of variance in dependent variable that can be predicted from independent variable. It is always between 0 and 1, inclusive. Solution 11: Correlation signifies the strength and direction of the linear relationship between two variables. If the correlation is positive, it signifies that when the independent variable increases, the dependent variable increases. But, it does not mean that X causes Y. For example, we can find a strong correlation between the number of smartphones in a city and the number of murders. But, this does not imply that the murders have increased due to the increase in smartphones. There could be a third variable which could cause increase in both the variables. This is the reason behind “correlation does not imply causation". At the point when there is a natural reason between two factors, at that 8 Robin Henson @ 2019-05-05T21:19:22-07:00 good, so why did you say r2 reflects causality above? point they will be corresponded. If neither A nor B causes the other, and the two are associated, there must be some normal reason for the two. Solution 12: Some of the possible reasons behind large correlations between two variables are: Linear relationship – The large correlation between two variables could be due to the strong linear relationship between the variables. A strong positive or negative linear relationship result in large correlation coefficient. Influential point – Many a times there is an influential data point which is far away from the other data points and it effect the correlation coefficient in a significant way, resulting in large correlation. Solution 17: The assumptions required for a correlation to be valid description of the relationship between two variables are: Level of measurement – Both the variables considered for correlation should be measured at least at interval level. Any variable measured at ordinal or nominal level cannot be considered for correlation calculation. Homoscedasticity – If there is a non-linear or mainly curvilinear relationship between the variables, we cannot calculate a valid correlation between the variables. Reference: Warner, R. M., Applied Statistics (2012). Thousand Oaks, CA. Sage Publications Group 9 Robin Henson @ 2019-05-05T21:21:03-07:00 outliers is one reason, but linear relationship really isn't. this is getting at what might be problems with the data that inflate the correlation. can you list some other reasons? Comment Summary Page 2 1. this is not what r2 tells us 2. not clear which, if any, correlations (r) you are saying are stat sig, which is what the question is asking. 3. not cleare what you are saying here, but need to state clearly what correlations are stat sig, if any, after invoking the alpha correction. 4. incorrect. 5. true, so why are you saying causal things above? 6. other things? outliers? homoscedasticity? 7. good, or when there are well controlled experimental designs, but that is a matter of research design, not statistical analysis. Page 3 8. good, so why did you say r2 reflects causality above? Page 4 9. outliers is one reason, but linear relationship really isn't. this is getting at what might be problems with the data that inflate the correlation. can you list some other reasons? NEXT PAGE MORE QUESTIONS