An instructor asked five students how many hours they had studied for an exam. (For part f, assume that hours studied is the predictor variable.) Here are the number of hours studied and the students' grades:
Hours Studied Test Grade
Do the following to solve the problem: (a) Make a scatter diagram of the raw scores; (b) describe in words the general pattern of association, if any; (c) figure the correlation coefficient; (d) explain the logic of what you have done, writing as if you were speaking to someone who has never had a statistics course (but who does understand the man, standard deviation, and Z scores); (e) give three logically possible directions of causality, saying for each whether it was a reasonable direction in light of the variables involved (and why); (f) make raw score predictions on the criterion variable for persons with Z scores on the predictor variable of -2, -1, 0, +1, and +2; and (g) give the proportion of variance accounted for (R2).
a) see attachment
b) Positive linear correlation - as hours studied goes up, so do test grades.
c) see attachment
d) The first step in a correlation problem is to make a graph, putting one variable on each axis, then putting a dot where each score falls on that graph. This is called a scatter diagram, and it gives a picture of the degree of relationship between the two variables. In this case, high scores seem to go with high scores, and lows with lows, making this what is called a positive correlation. (Basically, correlation is the extent to which high scores go with high scores and low scores go with low scores.) Also, because the dots fall roughly near a straight line, this is an example of a positive ...
The solution examines studying for exam statistics. It describes the patterns associated with how many hours spent studying versus final grades.