The Table Below Shows Data For $n = 20$ Observations A Use a First-Order Regression Model to Find a Least

question 126

Essay

The table below shows data for $n = 20$ observations.

$\begin{array}{ccc}\hline \mathrm{y} & \mathrm{x} 1 & \mathrm{x} 2 \\\hline 18 & 3 & 8 \\23 & 5 & 10 \\15 & 2 & 7 \\31 & 6 & 12 \\24 & 4 & 9 \\28 & 5 & 11 \\17 & 2 & 7 \\19 & 3 & 8 \\30 & 7 & 10 \\28 & 5 & 8 \\14 & 3 & 6 \\32 & 7 & 11 \\17 & 2 & 8 \\24 & 5 & 10 \\26 & 6 & 11 \\27 & 6 & 11 \\21 & 3 & 6 \\31 & 7 & 13 \\19 & 2 & 8 \\25 & 5 & 10 \\\hline\end{array}$

a. Use a first-order regression model to find a least squares prediction equation for the model.
b. Find a $95 \%$ confidence interval for the coefficient of $x _ { 1 }$ in your model. Interpret the result.
c. Find a $95 \%$ confidence interval for the coefficient of $x _ { 2 }$ in your model. Interpret the result.
d. Find $R ^ { 2 }$ and $R _ { a } 2$ and interpret these values.
e. Test the null hypothesis $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0$ against the alternative hypothesis $H _ { \mathrm { a } } :$ at least one $\beta _ { i } \neq 0$ . Use $\alpha = .05$ . Interpret the result.

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Definitions:

Cole and Scribner

Researchers who studied the influence of culture on memory and cognition, demonstrating differences in memory strategies between schooled and unschooled populations.

Depth Cues

Visual cues that allow individuals to perceive depth and distance, such as binocular disparity and linear perspective.

Carpentered Environments

Refers to physical spaces that are human-made and characterized by straight lines, right angles, and flat surfaces, influencing perception according to certain psychological theories.

Visual Illusions

Visual illusions are perceptions that differ from objective reality, illustrating how the brain processes visual information.