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 - 6294.729x - 2 348.037x2. 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.