# Psych 218

**Topics:**Regression analysis, Linear regression, Statistics

**Pages:**5 (1246 words)

**Published:**February 17, 2012

Marking of lab assignments will be very strict. If you did not complete the CogLab "Memory Span" experiment on time, you will lose 1/4 of the total assignment grade (6 points). To avoid receiving other deductions, type your answers in the spaces provided. You may insert additional spaces after any question as needed. In addition, use proper symbols and notation (e.g., sY/X, r, R) in all your answers. Properly round your final answers to 2 decimal places, with the following exception: Round regression line slopes (coefficients) and Y-intercepts (constants) to 3 decimal places. You will lose marks for each and every failure to follow these directions.

This lab assignment is due at the beginning of class on Tuesday February 14, but you have an automatic extension until the beginning of class on Thursday February 16. You must print out your completed assignment and attach (using a staple) any relevant SPSS output. Do not email your assignment. You will lose 1/8 of the total assignment grade (3 points) for each day it is late. An assignment will be considered one day late as soon as the lecture begins on Thursday February 16.

1. Perform a simple regression analysis using the frequency with which students took notes ('notes') to predict their mean grade ('meangrade'). [8 points]

a. Report the correlation between 'notes' and 'meangrade'. (1 point) r = 0.39

b. Provide a precise interpretation of the value of R squared given in the Output window. (1 point) The coefficient of determination (r2) is 0.15.

0.1553 x 100% = 15.53%

The variability of mean grades of the class (‘meangrade’) accounted for by the frequency which a student took notes (‘notes’) is 15.53%.

c. Using the results in the output window, construct and report the regression equation. (1 point) Y’ = -3.980X + 78.573

d. Using the regression equation from question 1 c, predict the mean grade of a student who reported 'rarely' taking notes last semester. Show your work. (1 point) Y’ = -3.980(4) + 78.573 = 62.65

The predicted mean grade of a student who reported rarely (‘rarely’) taking notes last semester according to the regression line would be 62.65.

e. Report the standard error of estimate and provide a precise interpretation of this value. (2 points) The standard error of estimate is 8.26. We can then expect our predictions of the mean grade of a student (‘meangrade’) to be off by about 8.26.

f. Explain why the regression coefficient (bY) is negative. (2 points) Thinking back on that the frequency with which a student took notes (‘notes’) is a nominal variable, which we coded numerically with ‘1’ as ‘always’ taking notes to ‘5’ as ‘never’ taking notes. The negative slope associated with this variable indicates that never taking notes (a higher value) is associated with a lower mean grade of the student (‘meangrade’).

2. Perform a multiple regression analysis using the frequency with which student took notes ('notes') and their motivation ('motivation') to predict their mean grade ('meangrade'). [8.5 points]

a. Report the multiple correlation. (1 point)

R = 0.64

b. What percentage of the variability in students' mean grades ('meangrade') can be accounted for by the frequency with which they took notes ('notes') and their motivation ('motivation')? (1 point) R2 = 0.41

0.4129 x 100% = 41.29%

The variability of mean grades of the class (‘meangrade’) accounted for by the...

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