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Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.





x
9
8
13
10
12
14
6
4
13
7
6



y
7.51
6.56
12.94
7.21
7.56
8.95
6.16
5.55
8.08
6.38
5.81




Create a scatterplot of the data. Choose the correct graph below.
A
B.
C.
D.
Find the equation of the regression line.

Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.\newline\begin{tabular}{cccccccccccc}\newline\hline x \mathbf{x} & 99 & 88 & 1313 & 1010 & 1212 & 1414 & 66 & 44 & 1313 & 77 & 66 \\\newliney \mathbf{y} & 77.5151 & 66.5656 & 1212.9494 & 77.2121 & 77.5656 & 88.9595 & 66.1616 & 55.5555 & 88.0808 & 66.3838 & 55.8181 \\\newline\hline\newline\end{tabular}\newlineCreate a scatterplot of the data. Choose the correct graph below.\newlineA\newlineB.\newlineC.\newlineD.\newlineFind the equation of the regression line.

Full solution

Q. Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.\newline\begin{tabular}{cccccccccccc}\newline\hline x \mathbf{x} & 99 & 88 & 1313 & 1010 & 1212 & 1414 & 66 & 44 & 1313 & 77 & 66 \\\newliney \mathbf{y} & 77.5151 & 66.5656 & 1212.9494 & 77.2121 & 77.5656 & 88.9595 & 66.1616 & 55.5555 & 88.0808 & 66.3838 & 55.8181 \\\newline\hline\newline\end{tabular}\newlineCreate a scatterplot of the data. Choose the correct graph below.\newlineA\newlineB.\newlineC.\newlineD.\newlineFind the equation of the regression line.
  1. Calculate Mean: Calculate the mean of xx-values (xˉ\bar{x}) and yy-values (yˉ\bar{y}).
  2. Calculate Slope: Calculate the slope bb of the regression line using the formula b=Σ[(xixˉ)(yiyˉ)]Σ[(xixˉ)2]b = \frac{\Sigma[(x_i - \bar{x})(y_i - \bar{y})]}{\Sigma[(x_i - \bar{x})^2]}.
  3. Calculate Y-Intercept: Calculate the y-intercept aa of the regression line using the formula a=yˉb×xˉa = \bar{y} - b \times \bar{x}.

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