The data on the left contains nutrition information on the number of Calories and grams of carbohydrates for 58 sandwiches and similar items on McDonald's menu. Problems 1. Run a regression of Calories (y-variable) on Carbs (x-variable). Be sure to include the scatterplot with the least squares line. 2. Interpret the slope of the regression in the context of the problem. 3. Interpret the R-square in the context of the problem. 4. Predict the number of calories for an item with 40 grams of carbohydrates. Type your answer in cell E4. Predicting Calories Carbs 40 Prediction Calories Carbs 780 55 420 34 520 45 290 33 600 47 480 35 290 30 290 35 230 30 680 45 420 35 560 53 740 42 400 40 250 31 230 24 240 32 370 33 450 47 790 56 520 41 640 42 530 57 410 45 330 32 460 27 920 53 180 11 280 16 350 39 380 37 470 45 610 58 400 44 370 40 620 67 580 67 310 30 420 47 640 50 550 66 510 66 290 25 290 30 520 67 470 67 170 28 290 62 160 16 600 106 400 37 390 64 350 64 710 56 420 47 370 32 430 32 540 49
Added by Crystal S.
Step 1
First, we need to run a regression of Calories on Carbs. We can use software like Excel, R, or Python to do this. I cannot create a scatterplot with the least squares line here, but I can provide you with the regression equation. After running the regression, we Show more…
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The number of calories in a food item depends on many factors, including the amount of fat in the item. The data below shows the amount of fat (in grams) and the number of calories in 7 beef sandwiches at McDonald's. The scatterplot displaying the relationship is shown to the right: Sandwich Fat Calories Big Mac 29 550 Quarter Pounder w/ Cheese 26 520 Dbl Quarter Pounder w/ Cheese 42 750 Hamburger 9 250 Cheeseburger 12 300 Double Cheeseburger 23 440 McDouble 19 390
David N.
In the last chapter, you examined the association between the amounts of Fat and Calories in fast-food hamburgers. Here are the data: $$ \begin{array}{|l|r|r|r|r|r|r|r|} \hline \text { Fat (g) } & 19 & 31 & 34 & 35 & 39 & 39 & 43 \\ \hline \text { Calories } & 410 & 580 & 590 & 570 & 640 & 680 & 660 \\ \hline \end{array}$$ a) Create a scatterplot of Calories vs. Fat. b) Interpret the value of $R^{2}$ in this context. c) Write the equation of the line of regression. d) Use the residuals plot to explain whether your linear model is appropriate. e) Explain the meaning of the $y$ -intercept of the line. f) Explain the meaning of the slope of the line. g) A new burger containing 28 grams of fat is introduced. According to this model, its residual for calories is +33 . How many calories does the burger have?
Burgers In the last chapter, you examined the association between the amounts of Fat and Calories in fast-food hamburgers. Here are the data: $$ \begin{array}{lccccccc}{\text { Fat }(g)} & {19} & {31} & {34} & {35} & {39} & {39} & {43} \\ {\text { Calories }} & {410} & {580} & {590} & {570} & {640} & {680} & {660} \\ \hline\end{array} $$ a) Create a scatterplot of Calories vs. Fat. b) Interpret the value of $R^{2}$ in this context. c) Write the equation of the line of regression. d) Use the residuals plot to explain whether your linear model is appropriate. e) Explain the meaning of the y-intercept of the line. f) Explain the meaning of the slope of the line. g) A new burger containing 28 grams of fat is introduced. According to this model, its residual for calories is +33. How many calories does the burger have?
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