MATH 1342 Elementary Statistical Methods Lab 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 graph! 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. 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 (in thousands of dollars) for a random sample of homes for sale in Naples, Florida, in December 2010. Square Asking Footage Price ($) 1148 154,000 1096 159,900 1142 169,000 1288 169,900 1322 170,000 1466 179,900 1344 180,000 1544 189,000 1494 189,900 Lab Ch. 4 continued a) On the axes above, draw a scatter diagram treating the square footage as the explanatory variable and asking price as the response variable. Label the graph! There is a linear relationship between the square footage and asking price. For each of the following, use the proper format for the monetary values. b) State the linear correlation coefficient c) Find the least-squares regression line. d) Predict the asking price if the square footage is 1500. e) Would a prediction for the asking price of a home that is 3350 square feet be reasonable? Why or Why not? Use a complete sentence and proper grammar. f) Interpret the slope. Use a complete sentence and proper grammar. g) Is it reasonable to interpret the y-intercept? Why or why not