Stat 4.2 least square regression

A rural college is considering constructing a windmill to generate electricity but is concerned over noise levels. A study is performed measuring noise levels (in decibels) at various distances (in feet) from the campus library, and a least squares regression line is calculated with a correlation of 0.74. Which of the following is a proper and most informative conclusion for an observation with a negative residual?

• (A) The measured noise level is 0.74 times the predicted noise level.

• (B) The predicted noise level is 0.74 times the measured noise level.

• (C) The measured noise level is greater than the predicted noise level.

• (D) The predicted noise level is greater than the measured noise level.

• (E) The slope of the regression line at that point must also be negative.

Problem 3-5 refer to the following: The relationship between winning game proportions when facing the sun and when the sun is on one’s back is analyzed for a random sample of 10 professional players. The computer printout for regression is below:

What is the equation of the regression line, where face and back are the winning game proportions when facing the sun and with back to the sun, respectively?

• (A) (facing) ̂ = 0.056 + 0.920 back

• (B) (back) ̂ = 0.056 + 0.920 facing

• (C) (facing) ̂ = 0.920 + 0.056 back

• (D) (back) ̂ = 0.920 + 0.056 facing

• (E) (facing) ̂ = 0.024 + 0.039 back

Problem 3-5 refer to the following: The relationship between winning game proportions when facing the sun and when the sun is on one’s back is analyzed for a random sample of 10 professional players. The computer printout for regression is below:

What is the correlation?

• (A) –0.984

• (B) –0.986

• (C) 0.984

• (D) 0.986

• (E) 0.993

Problem 3-5 refer to the following: The relationship between winning game proportions when facing the sun and when the sun is on one’s back is analyzed for a random sample of 10 professional players. The computer printout for regression is below:

For one player, the winning game proportions were 0.55 and 0.59 for facing and back, respectively. What was the associated residual?

• (A) –0.028

• (B) 0.028

• (C) –0.0488

• (D) 0.0488

• (E) 0.3608

In a study of winning percentage in home games versus average home attendance for professional baseball teams, the resulting regression line is:

(Winning percentage) ̂ = 44 +0.0003 （average homeattendance）

What is the residual if a team has a winning percentage of 55% with an average attendance of 34,000?

• (A) –11.0

• (B) –0.8

• (C) 0.8

• (D) 11.0

• (E) 23.0

Calculate Regression Line: we used data from a random sample of 15 high school students to investigate the relationship between foot length (in centimeters) and height (in centimeters).

The mean and standard deviation of the foot lengthsare x ̅  = 24.76 cm and s_x = 2.71 cm. The mean and standard deviation of the heights are y ̅ = 171.43 cm and s_y = 10.69 cm. The correlation between footlength and height is r = 0.697.

PROBLEM:

Find the equation of the least-squares regression line for predicting height from foot length. Show your work.

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In Section 3.l, we looked at the relationship between the average num-ber of points scored per game x and the number of wins y for the 12college football teams in the Southeastern Conference. A scatterplotwith the least-squares regression line and a residual plot are shown.Theequation of the least-squares regression line is=-3.75 + 0.437x.Also,s = 1.24 and r2 = 0.88.

PROBLEM:

(a) Calculate and interpret the residual for South Carolina, which scored 30.1 pointsper game and had 1 1 wins.

(b) Is a linear model appropriate for these data? Explain.

(c) Interpret the value of s.

(d) Interpret the value of r2

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A random sample of 15 high school students was selected from the U.S. CensusAtSchool database. The foot length (in centimeters) and height (in centimeters) of each student in the sample were recorded.

(a) What is the equation of the least-squares regression line that describes the relationship between foot length and height? Define any variables that you use.

(b) Find the correlation.

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