Statistics Linear Regression Worksheet



1. The decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper “Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids” gave the accompanying data on y = maximum size of salmonids consumed by a northern squaw fish and x = squawfish length, both in millimeters. The accompanying data is from MINITAB

The regression equation is

size = -89.1+0.729 length

Predictor Coef Stdev t-ratio p

Constant -89.09 16.83 -5.29 0.000

length 0.72907 0.04778 15.26 0.000

s=12.56 R-sq=96.3%

a) Interpret the slope in context of the problem

b) What is the correlation coefficient? Interpret this value.

c) What value of maximum size would you predict for a squawfish whose length is 375 mm?

d) What is the residual corresponding to the observation (375,165)? Interpret this value.

e) What proportion of observed variation in y can be attributed to the approximate linear relationship between the two variables?

2. Lydia and Bob were searching the Internet to find information on air travel in the U.S. They found data on the number of commercial aircraft flying in the U.S. during the years 1990-1998. The dates were recorded as years since 1990. Thus, the year 1990 was recorded as year 0. They fit a least-squares regression line to the data. Part of the computer output for their regression are given below.

a. What is the value of the slope of the least squares regression line?

Interpret the slope in the context of this situation.

b. What is the value of the intercept of the least squares regression line?

Interpret the intercept in the context of this situation.

c. What is the predicted number of commercial aircraft flying in 1992?

d. If the residual for 1992 is 40, what is the actual number of commercial aircraft flying in 1992?

3. An emergency service wishes to see whether a relationship exists between the high outside

temperature on a given day and the number of emergency calls it receives. They examine data from 10 randomly selected days last year. The data is as follows:

[pic]

a) Find the least squares regression line. State the equation below and interpret the slope and y-intercept

b) Find and interpret the value of r2.

c) Create a residual plot on your calculator. What does this plot tell you about a linear model for this data? How do you know?

d) Find and interpret the residual for 93°.

e) What point represents the largest residual? What does that residual mean?

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