Part of an Excel Output Relating X (Independent Variable) and Y

question 5

Essay

Part of an Excel output relating x (independent variable) and y (dependent variable) is shown below. Fill in all the blanks marked with a question mark. $\mathbf {Summary~ Output}$

$\mathbf {Regression~ Statistics}$
$\begin{array}{ll}\text { Multiple R } & 0.1347 \\\text { R Square } & ? \\\text { Adjusted R Square } & ? \\\text { Standard Error } & 3.3838 \\\text { Observations } & ?\end{array}$ ​ $\begin{array}{llllll} \mathbf { ANOVA}\\& \mathbf {d f} & \mathbf {S S} & \mathbf {M S} & \mathbf {F} & \mathbf {Significance ~F} \\\text { Regression } & ? & 2.750 & ? & ? & 0.6322 \\\text { Residual } & ? & ? & 11.45 & &\\Total&14&?\end{array}$ ​ $$\begin{array} { l l l l l } & \mathbf {Coefficients } & \mathbf { Standard~ Error } & \mathbf {t~ Stat } & \mathbf {P-value } \\\text { Intercept } & 8.6 & 2.2197 & ? & 0.0019 \\x & 0.25 & 0.5101 & ? & 0.6322\end{array}$$ ​

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Definitions:

Standard Deviation

A measure of the amount of variation or dispersion of a set of values; a low standard deviation means the values are close to the mean, while a high standard deviation means the values are dispersed over a wider range.

Standard Normal Random Variable

A random variable with a mean of zero and a variance of one, following the standard normal distribution.

Area

The measure of the extent of a two-dimensional surface or shape, expressed in square units.

Z

Often refers to a Z-score in statistics, representing the number of standard deviations a data point is from the mean.