Sum of squared residuals and R² Problem set B Answers

\(R^2\) = 0.894

\(R^2\) = 0.999

\(R^2\) = 0.993

1. (a) \(R^2\) = 0.764
2. (b) 76.4%

1. (a) 0.2, −0.2, 0.6, −0.3, 0.1
2. (b) 0.54

1. (a) \(P = -0.00447r^3 + 0.720r^2 + 11.8r - 19.1\)
2. (b) 2870
3. (c) r = 150 is outside the range of the data (6.8 to 36), so this is extrapolation and is not reliable. The cubic has a negative r³ coefficient: it reaches a maximum at r = 115 and then falls, but a satellite further from the Earth would not take less time to orbit it.

1. (a) 0.852
2. (b) 0.956
3. (c) The cubic has the larger \(R^2\) (0.956 against 0.852), so it explains more of the variation and fits better.

1. (a) 67.95
2. (b) 138.07
3. (c) Model 1: its \(SS_{res}\) (67.95) is smaller than the other (138.07)

1. (a) \(y=5.97t+214\), \(R^2\) = 0.950
2. (b) 453
3. (c) 40 is far outside the data range (0 to 10), so the prediction is extrapolation. House prices depend on wages, interest rates and supply, which do not follow one straight line for 40 years. The high \(R^2\) only describes the fit inside the data.