Last year, 20 randomly selected students at University of Florida took a math ap
ID: 3056367 • Letter: L
Question
Last year, 20 randomly selected students at University of Florida took a math aptitude test
before they began their Introductory Statistics course. The scores on the aptitude test ranged
from 60 to 95. The Statistics department would like to predict the final grade in the Statistics
class based on the score on the math aptitude test. The data is summarized below.
(a) Identify the predictor variable x and the response variable y. Write the full theoretical model, the model assumptions, and identify the parameters and estimators.
(b) Compute the LSR equation.
(c) Interpret the slope, the y-intercept, the correlation, and the R2.
(d) Predict the statistics grade for someone who scored 78 on the math aptitude test.
(e) Would we predict the statistics grade for someone who scored 35 on the aptitude test? Explain.
Aptitude Test Score Statistic Grade Correlation x bar = 74.5 y bar = 82.5 r = 0.763 Sx = 12.129 Sy = 13.079Explanation / Answer
SolutionA:
predictor variable x=Aptitude Test Score
and the response variable y. =Statistic Grade
the regrssion model is
Statistic Grade=b0+b1(Aptitude Test Score)
b0-y intercept
b1---slope
model assumptions are:
model is linear in parameters.
data are collected through indpendent random sampling.
there must be sample vraiation in the indpenedent variable.
.the error term has zero mean
the error term is uncorrelated with the independent variable and all functions of the independent variable.
error term has constant variance.
(b) Compute the LSR equation.
slope=b1=r SDy/SDx
b0=y bar-b1x bar
b1=0.763*13.079/ 12.129= 0.8227617
b0=82.5-0.8227617(74.5)
b0= 21.20425
the regression eq is
Statistic Grade=21.20425+0.8227617(Aptitude Test Score)
c) Interpret the slope, the y-intercept, the correlation, and the R2.
slope=0.8227617
Fro unit increase in (Aptitude Test Score) ,the predicted Statistic Grade incraeases by 0.8227617
y intercept=21.20425
with Aptitude Test Score=0 ,the Statistic Grade is21.20425
r sq=r*r=0.763*0.763=0.582169
58.169% varaition in Statistic Grade is explained by model .
Rest 100-58.169=41.831 variation is unexplained.
Solutiond:
78 on the math aptitude test.
We have
Statistic Grade=21.20425+0.8227617(Aptitude Test Score)
Statistic Grade=21.20425+0.8227617(78)
=85.37966
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