MATH 1342
Elementary Statistical Methods
Lab 3 – Ch.4 – Linear Regression
Name ___________________________
Critical Thinking; Communication Skills; Empirical/Quantitative Skills
1. Researchers wondered whether the size of a person’s brain was related to the individual’s mental
capacity. They selected a sample of right-handed introductory psychology students who had SAT
scores higher than 1350. The subjects took the Wechsler Adult Intelligence Scale-Revised to obtain
their IQ scores. MRI scans were performed at the same facility for the subjects. The scans consisted
of 18 horizontal MR images. The computer counted all pixels with a nonzero gray scale in each of the
18 images, and the total count served as an index for brain size.
MRI Count
816,932
951,545
991,305
833,868
856,472
852,244
790,619
866,662
857,782
948,066
IQ
133
137
138
132
140
132
135
130
133
133
a) On the axes above, draw a scatter diagram treating MRI count as the explanatory
variable and IQ as the response variable. Label the axes!
b) Test whether there is a linear relationship between MRI count and IQ.
c) Predict the IQ score for a subject who has an MRI count of 850,000.
Lab Ch. 4 continued
2. One of the biggest factors in determining the value of a home is the square footage. The
following data represent the square footage and asking price for a random sample of homes for sale
in Naples, Florida, in December 2010.
Square
Footage
1,148
1,096
1,142
1,288
1,322
1,466
1,344
1,544
1,494
Asking
Price ($)
154,000
159,900
169,000
169,900
170,000
179,900
180,000
189,000
189,900
As it turns out, there IS a linear relationship between the square footage and asking price.
When answering each of the following, use the proper format for the monetary values.
a) State the linear correlation coefficient.
(round to 3 decimals)
b) Find the least-squares regression line.
(round each number to 2 decimals)
c) Predict the asking price if the square footage is 1,500.
d) Would a prediction for the asking price of a home that is 3,350 square feet be reasonable?
Why or Why not? Use a complete sentence and proper grammar.
e) Interpret the slope. Use a complete sentence and proper grammar.
f) Is it reasonable to interpret the y-intercept? Why or why not? Use a complete sentence and
proper grammar.