The total amount of consumer credit has been increasing steadily in recent years

Question

The total amount of consumer credit has been increasing steadily in recent years. The following table gives the total outstanding consumer credit. Answer part a. through e. Find an equation for the least squares line, letting x equal the number of years since 2001. Use part a to find, at approximately what rate is the consumer credit growing per year? Use the result from part a to predict the amount of consumer credit in the year 2016. If this trend continues linearly, in what year will the total debt first exceed $4000 billion? Find and interpret the correlation coefficient. The equation is (Use integers or decimals for any numbers in the equation. Round to two decimal places as needed.)

Explanation / Answer

(a) y = 2049.54 + 93.03x

(b) It is growing at the rate of 93.03 billion dollars per year

(c) (n 2016 (x = 15), it is 3444.99 billion dollars

(d) y = 4000

x = (y - 2049.54)/93.03 = 20.96 (x = 21, that is year 2022)

(e) r = 0.991 implies there exists a high degree of correlation between x and y.

Regression Analysis r² 0.982 n   5 r   0.991 k   1 Std. Error   23.174 Dep. Var. y ANOVA table Source SS   df   MS F p-value Regression 86,545.8090 1   86,545.8090 161.15 .0011 Residual 1,611.1230 3   537.0410 Total 88,156.9320 4   Regression output confidence interval variables coefficients std. error    t (df=3) p-value 95% lower 95% upper std. coeff. Intercept 2,049.5400 0.000 x 93.0300 7.3283 12.695 .0011 69.7081 116.3519 0.991 Predicted values for: y 95% Confidence Interval 95% Prediction Interval x Predicted lower upper lower upper Leverage 15 3,444.9900 3,186.3371 3,703.6429 3,176.0282 3,713.9518 12.300

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