Two Questions: The Table Shows The Of Ice Cream Balance

Two Questions1 The Following Table Shows The Of Ice Cream Bars Sold

Two Questions 1. The following table shows the # of ice cream bars sold by a vendor as explained by the outside high temperature High Temperature for the day in degrees F # of bars of ice cream sold a) Find xx SS xy SS yy SS b) Write the equation of the line of best fit (the least square regression line) c) Use the line of best fit to predict the # of cups sold on a day with a high temperature of 70 degrees F. d) What is the value of the correlation coefficient between the two variables. e) What percentage of variation in the # of cups sold is explained by the line of best fit? f) Is the correlation significant at 5% level of significance? 2. Submit the answer of the question #10 on the page 595 of the text book. _.unknown _.unknown _.unknown

Paper For Above instruction

The relationship between temperature and the sales of ice cream bars provides a compelling illustration of statistical analysis, especially in understanding the nature and strength of correlation between two variables. In this paper, we will analyze a dataset that explores how high temperature influences the number of ice cream bars sold by a vendor, applying key statistical tools such as the least squares regression line, correlation coefficient, and significance testing to interpret the data comprehensively.

Imagine a dataset where the high temperatures of several days and the corresponding number of ice cream bars sold are recorded, say, for example, temperatures ranging from 60°F to 80°F and sales numbers varying accordingly. To understand the linear relationship between these two variables, we begin by calculating the sums of the cross-products (xy), the sums of squares for x (temperature), y (sales), as well as their means and deviations. These values allow us to compute the coefficients needed for the least squares regression line, which minimizes the sum of squared differences between observed and predicted values.

The first step involves calculating the slope (b) and intercept (a) of the regression line. The slope indicates how much the sales of ice cream bars increase with each degree rise in temperature, while the intercept estimates sales at zero temperature. The formulas for these are based on the sums of xx (temperature deviations squared), xy (product of deviations), and yy (sales deviations squared). For example, the slope can be written as b = SS_xy / SS_xx, and the intercept as a = ȳ - b * x̄, where x̄ and ȳ are the means of temperature and sales, respectively.

Once the regression equation is established, it can be used to predict sales on specific days, such as a day with a high temperature of 70°F. Plugging x = 70 into the equation provides an estimate of the number of ice cream bars likely to be sold, serving as a practical application of the statistical model.

Furthermore, assessing the strength of the relationship involves calculating the correlation coefficient (r), which quantifies the degree of linear association between temperature and sales. The value of r ranges from -1 to 1, where values close to 1 or -1 indicate strong positive or negative linear relationships, respectively. Its square (r²) represents the coefficient of determination, which explains the proportion of variability in sales attributable to temperature. For example, an r² of 0.85 implies that 85% of the variation in ice cream sales can be explained by temperature changes.

To determine whether the correlation is statistically significant, hypothesis testing is performed at a specified significance level, such as 5%. This involves calculating a t-statistic based on r, the sample size, and degrees of freedom, then comparing it to a critical t-value. A significant correlation suggests that the association is unlikely to be due to random chance, reinforcing the predictive power of the model.

Finally, interpreting the results provides insights into sales strategies, such as forecasting demand on hot days and adjusting inventory or marketing efforts accordingly. The statistical analysis underscores how temperature impacts consumer behavior and aids business decisions.

In conclusion, analyzing the temperature-sales relationship through regression analysis, correlation assessment, and significance testing offers valuable understanding not only for vendors but also for broader applications in environmental and economic studies. Accurate models enable better planning, resource allocation, and performance evaluation, highlighting the importance of statistical literacy in data-driven decision-making.

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