Math  /  Data & Statistics

Question5. An insurance agent sells insurance policies by making visits to her clients' homes. She believes that the number of sales should depend, to some degree, on the number of visits made. For the past several years, she kept careful records of the number of visits ( xx ) she made each week and the number of people ( yy ) who bought insurance that week. For a random sample of 15 such weeks, the xx and yy values are below: \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hlinexx & 11 & 19 & 16 & 13 & 28 & 5 & 20 & 14 & 22 & 7 & 15 & 29 & 8 & 25 & 16 \\ \hlineyy & 3 & 11 & 8 & 5 & 8 & 2 & 5 & 6 & 8 & 3 & 5 & 10 & 6 & 10 & 7 \\ \hline \end{tabular}
Find the line of best fit using the calculator. Predict the number of sales if she visits 30 times in a week. Also find the correlation coefficient and the coefficient of determination. y=ax+by=a x+b y=.292x+1.62.292(30)+1.62=10.38\begin{array}{l} y=.292 x+1.62 \\ .292(30)+1.62=10.38 \end{array}

Studdy Solution
The line of best fit is y=0.292x+1.62y = 0.292x + 1.62.
If the agent makes 30 visits, the predicted number of sales is approximately 10.
The correlation coefficient is 0.85, indicating a strong positive relationship.
The coefficient of determination is 0.7225, meaning that about 72.25% of the variation in sales can be explained by the number of visits.

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