Examples of regression and probability (taken from the “second activity” in December 2015)

Statement for Questions 1 to 6: We have a database with demographic variables and variables related to well-being, optimism, pessimism, among others. It is available at the following link http://www.uv.es/mperea/bienestar2.sav

Question 1. A) What type of relationship can you see between "Optimism" and "Pessimism"? (Use the appropriate graph; copy/paste); B) How would you quantify this relationship?; C) What proportion of variance is shared by both variables?

Question 2. A) What type of relationship can you see between "well-being" and "positive affect PANAS"? (Use the appropriate graph; copy/paste); B) How would you quantify this relationship?; C) What proportion of variance is shared by both variables? Indicate the appropriate output from SPSS

Question 3. A) What is the relationship between "Optimism" and "Pessimism" when you control for the influence of well-being? B) And when well-being is not controlled? C) What do this differences (of lack of thereof) between A) and B) mean?

Question 4. We want to predict the variable "satisfaction with life" from the predictors "Age" and "Optimism". A) What percentage of variance of "satisfaction with life" can be explained by the regression equation with the above-cited predictors? B) Can we have collinearity problems? Explain your answer.

Question 5. We want to predict the variable "satisfaction with life" from the predictors "well-being ", "pessimism" and "optimism". A) What percentage of variance of "satisfaction with life" can be explained by the regression equation with the above-cited predictors?; B) Can we have collinearity problems? C) Which one is the best predictor? (And why) Explain your answer.

Question 6. We want to predict the variable "satisfaction with life" from the predictors "well-being", "Age" and "Optimism". A) What percentage variance of "satisfaction with life" can be explained by the regression equation with these three predictors? B) If we perform the stepwise regression, what predictors enter the equation? What differences are there with respect to the previous question (i.e., A) regarding the percentage of variance explained? Explain your answer.

Question 7. The probability of finding a correct identification of agoraphobia is 0.95 in experienced psychologists. Let us think that, independently, 4 psychologists evaluate a person who (we know with complete confidence) has agoraphobia. Indicate the following: A) What is the probability that the four psychologists will indicate the correct diagnosis? B) What is the probability that at least one psychologist will be able to indicate the correct diagnosis?

Question 8. We have a probability density function defined as follows: f (x) = a for 0 <x <4 and f (x) = 0 for all other values. Indicate the following: A) the value of "a"; B) the value of (2); C) the value of f(2).

Question 9. We have the following game. You pay € 5 to play each time, and then you roll a die. If a "1" comes out they give us € 15; If there is a "2" they give us € 8; If you get a "3",they give us 7 EUR; And in the other scenarios they give us nothing. Is it worth playing this game? Explain your answer.

Question 10. In Spain, let’s assume that approximately 50% of people use glasses/contact lenses. Let's now assume that we travel to a country named X, and we see that of 100 people we have met, 70 of them wear glasses/contact lenses. Can we maintain the hypothesis that the proportion of people with glasses is similar in Spain and in country X? (Using the 95% Percentile as the criterion) Explain your answer.

Question 11. A person occupies the 40th percentile in a given test. Knowing that the test scores follow a normal distribution with a mean of 50 and a standard deviation of 5, what is the direct score of that individual?

Question 12. We want to know the percentage of people who have a score between 85 and 115 on an IQ test. We assume that IQ follows approximately a normal distribution with mean 100 and standard deviation 15.

Question 13. We have a probability density function defined as follows: f (x) = 0.5 for 0 <x <a and f (x) = 0 for all other values. Indicate the following: A) the value of "a"; B) the value of F(1); C) the value of f(1).

Question 14. We have the scores of the initial aptitude test when trying to get a job at a research center. We know that the data follow approximately a normal distribution with mean of 60 and standard deviation of 10. Only the best 10% of the participants will advance to the second test. What score will be used as a cut-off point?