Please help, thank you!!
A researcher measures how positive a person’s mood is and how creative he or she is, obtaining the following interval scores:
Participant Mood X Creativity Y
1 10 7
2 8 6
3 9 11
4 6 4
5 5 5
6 3 7
7 7 4
8 2 5
9 4 6
10 1 4
(a) Compute the statistic that summarizes this relationship. (b) What is the predicted creativity score for anyone scoring 3 on mood? (c) If your prediction is in error, what is the amount of error you expect to have? (d) How much smaller will your error be if you use the regression equation than if you merely used the overall mean creativity score as the predicted score for all participants?
(FYI: The number columns get messed up when I post, but it should be for example: 1 under participant, 10 under Mood X, and 7 under Creativity Y and son on)
To summarize the relationship between the mood and creativity scores, we can use regression analysis. This will help us determine the equation of the line that best fits the data points and allows us to make predictions.
(a) Compute the statistic that summarizes this relationship:
To compute the statistic that summarizes this relationship, we need to perform a regression analysis. This involves calculating the regression equation, which represents the line of best fit for the data. We can use this equation to predict creativity scores based on mood scores.
(b) Predicted creativity score for a mood score of 3:
To predict the creativity score for a mood score of 3, we need to use the regression equation obtained from the regression analysis. The regression equation will have the form Y = a + bX, where Y represents the predicted creativity score and X represents the mood score. The coefficients a and b can be obtained from the regression analysis.
(c) Amount of prediction error:
In regression analysis, there is always some degree of error in our predictions. To quantify the amount of error we expect to have, we can calculate the standard error of estimate (SEE) or the residuals. The SEE measures the average amount by which the actual scores deviate from the predicted scores. A smaller SEE indicates less prediction error.
(d) Error reduction using regression equation:
To determine how much smaller the error will be when using the regression equation compared to using the overall mean creativity score as the predicted score for all participants, we can compare the SEE for both scenarios. By incorporating the individual mood scores into the regression equation, we can account for variability in creativity scores based on mood, resulting in a more accurate prediction compared to simply using the mean.
To obtain the exact numbers and calculations, you would need to input the data into statistical software or use a statistical calculator that can perform regression analysis.