My purpose is to predict the number of calories per cookie based on the amount of saturated fat (g) per cookie. The scatterplot shows there is a strong positive association between the amount of saturated fat per cookie (x) and the number of calories per cookie (y). This observation is confirmed by the value of r, .850. According to the 1.5*IQR rule as applied to the residuals, there is one outlier. This outlier has the value 2g of saturated fat, 139 calories. This point could also possibly be an influential, however when I did the regression line without that point, there was very little difference between the graph with the point and the one without it. There was also only a difference of .05 between the two r values. Also, the difference in r values was only .05 proving that the point 2g saturated fat, 139 calories has little influence on the regression line. The r^2 value of .722 tells me that approximately 72.2% of the variation in the number of calories can be accounted for by the linear model. This also tells me that the least squares linear regression line fits the data fairly well. The residual plot shows no curved pattern so the linear model was an appropriate choice to fit the data. Using the least squares linear regression line, with the equation predicted y= 31.9 + 29.0x, I can predict the number of calories in a cookie by multiplying the number of grams of saturated fat in a cookie by 29.0, then adding 31.9. The slope of 29.0 means that for each increase of 1 gram of saturated fat, there is a corresponding increase of 29.0 calories per cookie. The residual plot shows that as the amount of saturated fat increases, my predictions become less accurate because the residuals towards the end of the graph (greater than 2.5g) are farther away from the line than those with the lower saturated fat(less than 2.5g). This relationship would be beneficial to consider when buying your next bag of cookies because if you see a high number of grams of saturated fat, you could estimate that the amount of calories would be high as well, and vice versa. Another observation I made when looking at my data was that all of the Chips Ahoy cookies, with the exception of the Peanut Butter Chunky, had 1.5g of saturated fat or less, and all of the Keebler brand cookies had saturated fat values of 1.5g and above. This could possibly suggest that Chips Ahoy cookies are healthier than Keebler cookies.
October 25, 2010