Math  /  Data & Statistics

QuestionA property analyst wishes to investigate the relationship between the town coundi's valuation of residential property in Johannesburg and the market value (current selling price in R 100.000) of properties. A random sample of 13 recent property transactions was examined. \begin{tabular}{|c|c|} \hline Council valuation & Markel value \\ \hline 1659 & 1850 \\ \hline 1920 & 2000 \\ \hline 1900 & 1959 \\ \hline 1200 & 1400 \\ \hline 1000 & 1200 \\ \hline 850 & 1000 \\ \hline 780 & 920 \\ \hline 870 & 990 \\ \hline 915 & 1100 \\ \hline 820 & 978 \\ \hline 1300 & 1700 \\ \hline 1500 & 1900 \\ \hline 1700 & 1850 \\ \hline \end{tabular}
4. 1 Define the independent and the dependent variabies 4.2 Draw a scatter plot to portrait the relationstip between independent variables and the Gependent variabies. interpret the scatter piot 43 Find the equation of the regression line describing the best fit of the relationship 44 Calculate the coefficient of correlation
4. 5 find the cocflicient of determination A.5 Estimate the market value of properties in fohannestburg that have a counctif variation of R 1200 (in R100\mathbf{R} 100 000) 4 interpret the meaning of the cosflicient of regression coetlicent (8,4)(8,4)

Studdy Solution
} \textbf{}
Interpret the meaning of the regression coefficient (slope bb).
\begin{itemize} \item The slope bb represents the change in market value for each unit change in council valuation. \end{itemize}
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\textbf{Solution:} \begin{itemize} \item The regression line is in the form y=a+bxy = a + bx. \item The coefficient of correlation indicates the strength and direction of the linear relationship. \item The coefficient of determination shows how much of the variation in the dependent variable is explained by the independent variable. \item The estimated market value for a council valuation of R 1200 can be calculated using the regression equation. \item The slope bb shows the effect of council valuation on market value. \end{itemize}

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