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=  192 eyes; the dependent variable was cone cell packing density (cells/mm2 ), and the two independent variables were x₁ = eccentricity (mm) and x₂ = axial length (mm).

a. The reported coefficient of multiple determination was .834. Interpret this value, and carry out a test of model utility.

b. The estimated regression function was y = 35,821.792 - 6294.729_x - 2 348.037_x2. Calculate a point prediction for packing density when eccentricity is 1 mm and axial length is 25 mm. c. Interpret the coefficient on x₁ in the estimated regression function in (b).

d. The estimated standard error of ß₁ was 203.702. Calculate and interpret a confidence interval with confidence level 95% for ß₁.

e. The estimated standard error of the estimated coefficient on axial length was 134.350. Test the null hypothesis H0: ß₂ = 0 against the alternative Ha: ß₂ ≠ 0 using a significance level of .05, and interpret the result.