Math Solutions

[All Steps] For this question, use the data in the following table. The table lists the personal income and outlays in trillions of dollars for Americans for

Question: For this question, use the data in the following table. The table lists the personal income and outlays in trillions of dollars for Americans for 11 recent years.

Personal Personal
income, x outlays, y
4.5 3.7
4.9 4.0
5.0 4.1
5.3 4.3
5.6 4.6
5.9 4.8
6.2 5.1
6.5 5.4
7.0 5.7
7.4 6.1
7.8 6.5
  1. Construct a scatter plot for the data on the grid below. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation?
  2. Calculate the correlation coefficient r. What can you conclude?
  3. Using a t-test, test the level of significance of the correlation coefficient r. Use a = 0.05.

d. Find the equation of the regression line for the data.

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -0.12925 0.074573 -1.73317 0.117101 -0.29794 0.039448
x 0.842991 0.012233 68.9135 1.44E-13 0.815319 0.870663

The table above shows that the regression equation is equal to:

\[y=-0.12925+0.842991x\]

(e) Use the regression equation to predict the personal outlays when the personal income is 5.3 trillion dollars.

f. Find the coefficient of determination and interpret the results.

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