The Following Data Show the Results of an Aptitude Test

question 27

Essay

The following data show the results of an aptitude test Y) and the grade point average of 10 students.
$\begin{array}{ll}\text { Aptitude Test }\\\text { Score Y) }&\text { GPA X) }\\26 & 1.8 \\31 & 2.3 \\28 & 2.6 \\30 & 2.4 \\34 & 2.8 \\38 & 3.0 \\41 & 3.4 \\44 & 3.2 \\40 & 3.6 \\43 & 3.8\end{array}$
a. Develop a least squares estimated regression line.
b. Compute the coefficient of determination and comment on the strength of the regression relationship.
c. Is the slope significant? Use a t test and let α = 0.05.
d. At 95% confidence, test to determine if the model is significant i.e., perform an F test).

---

Definitions:

Ponzo Illusion

A visual illusion where two horizontal lines of identical length appear different in length because of converging parallel lines in the background.

Necker Effect

An optical illusion related to the perception of a two-dimensional drawing of a cube, which can spontaneously appear to switch orientation.

McCullough Effect

A phenomenon where prolonged exposure to colored gratings causes the visual system to adapt and see complementary colors in grayscale patterns.

Perceptual Constancies

The tendency to perceive objects as unchanging, despite changes in sensory input, such as changes in illumination, angle, or distance.