Question

In: Statistics and Probability

A researcher wants to determine if there is a linear relationship between height and weight. The...

A researcher wants to determine if there is a linear relationship between height and weight. The following table represents the data collected. Display the data in a scatter plot on your calculator, draw a quick sketch below. Then find the linear regression and put the line of best fit on the sketch. Then state the value for the correlation coefficient and determine if this is a positive correlation or no correlation using the table in the back of the book.

Age in years

10

15

45

32

66

75

81

55

45

Height in feet

4

5.7

5.5

5.2

6

5.2

5.1

5.9

5.8

Solutions

Expert Solution

Age X Height Y X * Y
10 4 40 100 16
15 5.7 85.5 225 32.49
45 5.5 247.5 2025 30.25
32 5.2 166.4 1024 27.04
66 6 396 4356 36
75 5.2 390 5625 27.04
81 5.1 413.1 6561 26.01
55 5.9 324.5 3025 34.81
45 5.8 261 2025 33.64
Total 424 48.4 2324 24966 263.28

Correlation Coefficient



r = 0.358

Equation of regression line is


b = 0.009



a =( 48.4 - ( 0.0088 * 424 ) ) / 9
a = 4.964
Equation of regression line becomes


Since the value of r = 0.358 is positive and week, hence we conclude that there is week and positive correlation between two variables.


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