MATH 141 Least Squares Regression Practice Problems



MATH 141 Least Squares Regression Practice Problems

1. The mathematics department wants to predict the number of students enrolling in freshman level math courses (y) based upon the number of entering first-time freshmen (x). The data for recent years are:

|Year |1999 |2000 |2001 |2002 |2003 |2004 |2005 |2006 |

|X |4595 |4827 |4427 |4258 |3995 |4330 |4265 |4351 |

|Y |7364 |7547 |7099 |6894 |6572 |7156 |7262 |7450 |

Finding the LSR directly using the calculator

a. Enter the X data into L1 and the Y data into L2. Use the LinReg(a+bx) function to calculate the values of a, b, r, and r2. Write down all four of these values and the LSR for this data:

a = _________ b = __________ r = ____________ r2 = ___________ LSR: ______________________________

Describe the linear relationship between number of entering first-time freshmen and enrollment in freshman math courses.

Calculating r:

b. Enter the X data into L1 and the Y data into L2. Calculate the 2-variable statistics of:

[pic] = ______ sx = ______ [pic] = _____ sy = ______

c. Use L3 and L4 to calculate the z-scores for each X and Y value respectively.

d. Use L5 to calculate the products of the z-scores in L3 and L4.

e. Use the 1-variable stat function to calculate the sum of the products in L5. This is [pic]. _________

f. Calculate r by dividing your answer to part d by n-1. r = _________ Calculate r2 = _________. These should be very close to what the calculator gave you in part a.

Calculating the Least Squares Regression Line:

g. Calculate the value of b = ___________. Calculate the value of a = __________

h. Write the LSR: __________________________

Your answers to parts g and h should be very close to the values the calculator gave you in part a.

i. Interpret the meaning of r2.

j. There will be 4650 first time freshmen entering the university in the fall of 2007. Use the LSR to predict the enrollment in freshman math courses for the fall of 2007.

2. Does the age in months (X) at which a child begins to talk predict later score on an IQ test (Y)? Data from 21 children gave the following:

[pic] = 14 sx = 8 [pic] = 94 sy = 14 [pic] = –12

a. Calculate: r = __________ r2= ____________ a= ___________ and b= ___________

b. Describe the linear relationship between the age in months at which a child begins to talk and IQ test score.

c. Interpret the value of r2.

d. Predict the IQ score of a child who begins to talk at age 12 months.

e. One of the children in the sample began talking at age 12 months and later had an IQ score of 105. Does the actual data point of (12, 105) lie above, on, or below the LSR? How do you know this?

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