Stat 120Correlation and Regression Problems

1. Researchers at the European Centre for Safety Testing are trying to find out how the age of cars affects their braking capacity. They test a group of ten cars of differing ages and find out the minimum stopping distances that the cars can achieve. The following results were observed:

CarABCDEFGHIJ

Age (mths.)(x)9152430384653606476

Minim.Stopping Distance (y)28.429.337.636.236.535.336.244.144.847.2

Summary Statistics :

Recall :

and

(a) Draw a scatter plot to illustrate the above data. Comment on plot.

(b) Calculate the correlation coefficient, r. Comment on value of r.(c) Calculate the regression equation. 2. The following data show a sample of ten persons annual incomes and their corresponding years of formal education.

Yrs. of Education (x)19201616181214121617

Income(y)

(Thousands of Dollars)1251004035412935245060

Summary Statistics :

(a) Draw a scatter plot to illustrate the above data. Comment on plot.

(b) Calculate the correlation coefficient, r. Comment on value of r.

(c) Calculate the regression equation .

3. In an experiment, rats were placed in a shuttle box (maze) and were timed in successive attempts. An unsuccessful attempt was followed by an electric shock for the duration of the next attempt if an attempt was longer than 5 seconds. The data give the average times to complete the maze in seconds and the number of shocks for all attempts.Shocks (x)012345678910

Time (y)11.411.97.114.25.96.15.43.15.74.44.0

Shocks (x)1112131415

Time (y)2.82.62.45.22.0

Summary Statistics

(a) Draw a scatter plot to illustrate the above data. Comment on plot.

(b) Calculate the correlation coefficient, r. Comment on value of r.

(c) Calculate the regression equation .

4. The following data are the heights of 11pairs of brothers and sisters (ins).

1234567891011

Brother s height(x)7168666770717073726566

Sisters height (y)6964656365626564665962

(a) Draw a scatter plot to illustrate the above data. Comment on plot.

(b) Calculate the correlation coefficient, r. Comment on value of r.

(c) Calculate the regression equation .

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