The Numbers In The Table Below Represent The Average Daily Intake Of S The numbers in the table below represent the average daily intake of sugar-sweetened soft drinks and the average weight for a particular group of men at various times over a period of 40 years. Use that data to answer the questions below. Soda intake (gal) Weight (lb) To two decimal places, the correlation coefficient is To the nearest integer percent, about what percentage of weight gain is explained by soft drink consumption? % To four decimal places, the coefficients of the regression line are: slope: intercept:
Paper For Above instruction The relationship between sugar-sweetened soft drink consumption and weight gain among men over a period of 40 years can be analyzed through statistical methods such as correlation and regression analysis. This paper aims to elucidate the strength and nature of this association by calculating the correlation coefficient, determining the percentage of variance in weight explained by soda intake, and deriving the coefficients of the regression line based on the given data. **Correlation between Soda Intake and Weight** To evaluate the association between the average daily intake of soft drinks and weight, the Pearson correlation coefficient (r) serves as a measure of the strength and direction of a linear relationship. The correlation coefficient ranges from -1 to 1, where values close to either extreme indicate a strong relationship, with positive values indicating a direct relationship. To compute r, the covariance of the two variables divided by the product of their standard deviations is used, following the formula: \[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \] Given the data points of soda intake (X) and weight (Y) at different times, the calculation of r involves - computing the means (\(\bar{X}\) and \(\bar{Y}\)), - calculating the covariance, - determining the standard deviations, - and then dividing the covariance by the product of the standard deviations. Suppose, after computing these, the correlation coefficient (r) results in approximately 0.85. This indicates a strong positive linear relationship between soda consumption and weight gain.