Chapter 13.4, Problem 41E

The article “A Study of Factors Affecting the Human Cone Photoreceptor Density Measured by Adaptive Optics Scanning Laser Opthalmoscope” (Exptl. Eye Research, 2013: 1–9) included a summary of a multiple regression analysis based on a sample of n 5 192 eyes; the dependent variable was cone cell packing density (cells/mm2), and the two independent variables were x1 5 eccentricity (mm) and x2 5 axial length (mm).

1. a. The reported coefficient of multiple determination was .834. Interpret this value, and carry out a test of model utility.
2. b. The estimated regression function was y = 35,821.792 ‒ 6294.729x₁ ‒ 348.037x₂. Calculate a point prediction for packing density when eccentricity is 1 mm and axial length is 25 mm.
3. c. Interpret the coefficient on x₁ in the estimated regression function in (b).
4. d. The estimated standard error of $\hat{\beta }$₁ was 203.702. Calculate and interpret a confidence interval with confidence level 95% for $\hat{\beta }$₁.
5. e. The estimated standard error of the estimated coefficient on axial length was 134.350. Test the null hypothesis H₀: $\hat{\beta }$₂ = 0 against the alternative Ha: $\hat{\beta }$₂ ≠ 0 using a significance level of .05, and interpret the result.