For This Question, Use the California Testscore Data Set and Your

question 42

Essay

For this question, use the California Testscore Data Set and your regression package (a spreadsheet program if necessary). First perform a multiple regression of testscores on a constant, the student-teacher ratio, and the percent of English learners. Record the coefficients. Next, do the following three step procedure instead: first, regress the testscore on a constant and the percent of English learners. Calculate the residuals and store them under the name resYX2. Second, regress the student-teacher ratio on a constant and the percent of English learners. Calculate the residuals from this regression and store these under the name resX1X2. Finally regress resYX2 on resX1X2 (and a constant, if you wish). Explain intuitively why the simple regression coefficient in the last regression is identical to the regression coefficient on the student-teacher ratio in the multiple regression.

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Definitions:

Perceptual Errors

are mistakes in judgment that occur when an individual misinterprets sensory stimuli and information from the environment.

Stereotyping

Assigning fixed, generalized attributes to a group of people, often leading to prejudice and discrimination.

Discrimination

Unfair or prejudicial treatment of individuals based on certain characteristics such as race, gender, age, or sexual orientation, rather than on their merits.

Halo Effect

A cognitive bias where one's overall impression of a person, brand, or product influences one's thoughts and feelings about that entity's character or properties.