In: Statistics and Probability
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 |
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.