A researcher desires to know if the age of a child is related to the number of cavities the child has. The data are shown in the table below. Age of Child, x: 6, 8, 9, 10, 12, 14 Number of cavities, y: 1, 3, 4, 5, 6, 5 Given that x? = 9.8333, sx = 2.8577, y? = 4, sy = 1.7889, the researcher finds that the value of the correlation coefficient is 0.8607 and is statistically significant. A. Find the slope of the least squares regression line for predicting the number of cavities from the age of a child (Round your answer to four decimal places) B. Find the y-intercept of the least squares regression line for predicting the number of cavities from the age of a child (Round your answer to four decimal places) C. Construct the least squares regression line and use it to predict the number of cavities that a 13 year old has (Round your answer to four decimal places)
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The formula for the slope is: b = r * (σy / σx) where r is the correlation coefficient, σy is the standard deviation of the y-values (number of cavities), and σx is the standard deviation of the x-values (age of child). Substituting the given values into the Show more…
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