Professor Gill has taught General Psychology for many years. During the semester, she gives three multiple-choice exams, each worth 100 points. At the end of the course, Dr. Gill gives a comprehensive final worth 200 points. Let x1, x2, and x3 represent a student's scores on exams 1, 2, and 3, respectively. Let x4 represent the student's score on the final exam. Last semester Dr. Gill had 25 students in her class. The student exam scores are shown below.x1x2x3x47380751529388931858991901809698100196736670142534655101697477149475660115877990175797088164697073141706574141939591184798073152707378148938996192787568147819093183889286177788377159828690177868289175788385175768371149969395192 a) Perform a regression analysis with x4 as the response variable. Use x1, x2, and x3 as explanatory variables. Look at the coefficient of multiple determination. What percentage of the variation in x4 can be explained by the corresponding variations in x1, x2, and x3 taken together? (Use 1 decimal place.) ________ %b) Write out the regression equation. (Use 2 decimal places.)x4 = _____+ _____ x1 + _____ x2 + ____ x3

A regression equation is used to relate the response variable with one or more explanatory variable.…

Answered: Professor Gill has taught General…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter7: Systems Of Equations And Inequalities

Section7.2: Systems Of Linear Equations: Three Variables

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Professor Gill has taught General Psychology for many years. During the semester, she gives three multiple-choice exams, each worth 100 points. At the end of the course, Dr. Gill gives a comprehensive final worth 200 points. Let x₁, x₂, and x₃ represent a student's scores on exams 1, 2, and 3, respectively. Let x₄ represent the student's score on the final exam. Last semester Dr. Gill had 25 students in her class. The student exam scores are shown below.

x₁	x₂	x₃	x₄
73	80	75	152
93	88	93	185
89	91	90	180
96	98	100	196
73	66	70	142
53	46	55	101
69	74	77	149
47	56	60	115
87	79	90	175
79	70	88	164
69	70	73	141
70	65	74	141
93	95	91	184
79	80	73	152
70	73	78	148
93	89	96	192
78	75	68	147
81	90	93	183
88	92	86	177
78	83	77	159
82	86	90	177
86	82	89	175
78	83	85	175
76	83	71	149
96	93	95	192

a) Perform a regression analysis with x₄ as the response variable. Use x₁, x₂, and x₃ as explanatory variables. Look at the coefficient of multiple determination. What percentage of the variation in x₄ can be explained by the corresponding variations in x₁, x₂, and x₃ taken together? (Use 1 decimal place.) ________ %

b) Write out the regression equation. (Use 2 decimal places.)