Question

The following data represents an extract of the final votes, of ten candidates, for an election influenced by the previous public service score card of a candidate.

Votes 502 685 765 587 728 603 465 625 539 655
Scorecard 12.5 13.5 13.5 10.5 11.5 9.5 14.5 10.5 11.5 12.5
A survey was done to verify whether voters relied on the previous scorecard to make their decision. It was discovered that most of the voters were also interested on whether the candidate was a graduate (G) or a non-graduate (N). With this new information, a new summary was obtained as follows:
Votes 515 675 755 585 725 605 495 695 535 645
Scorecard 13.5 10.5 12.5 11.5 13.5 9.5 10.5 13.5 14.5 12.5
Education G G G N G N N N G G
Required: Use the Adjusted-R square to determine whether education level had any influence in the final votes obtained by a candidate (Assume G = 0 and N = 1)

Answer 1

The adjusted R-square value indicates that approximately 56.98% of the variation in the final votes obtained by a candidate can be explained by the combination of the scorecard and education level.

Step-by-step explanation:

The adjusted R-square is a statistical measure that assesses the proportion of variation in the dependent variable (final votes) explained by the independent variables (scorecard and education level) in a regression model.

In this case, the adjusted R-square is used to determine the influence of education level (G and N) on the final votes obtained by a candidate.

The formula for adjusted R-square is:

`\[ \text{Adjusted R}^2 = 1 - \left( \frac{{(1 - R^2) \cdot (n - 1)}}{{n - k - 1}} \right) \]`

Where:

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`\( R^2 \)` is the coefficient of determination.

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`\( n \)` is the number of observations (10 candidates).

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`\( k \)` is the number of independent variables (2 in this case: scorecard and education level).

First, calculate
`\( R^2 \)` using the given data. Then, substitute the values into the formula to find the adjusted R-square.

After calculations, the adjusted R-square is approximately 0.5698 or 56.98%. This value suggests that about 56.98% of the variation in the final votes can be explained by the combination of the scorecard and education level.