Part 1: Enjoying a beverage at Starbucks A lot of nutritional information is available for the foods and beverages we consume. How exactly do the ingredients in food and beverages relate to each other? Let's examine this by focusing on the caloric and carbohydrate content of a random sample of Starbucks' beverages. The number of calories and the number of grams of carbohydrates were recorded for a random sample of 50 different beverages from Starbucks. This data is shown in the scatterplot below. When a regression equation was constructed in order to predict grams of carbohydrates based on number of calories, the equation was as follows: Predicted grams of carbohydrates = 1.80 + 0.16 (number of calories) The correlation between number of calories and grams of carbohydrates is r = 0.93 8 8 8 Carbohydrates (in grams) 8 100 200 300 400 500 Calories Use the information above to answer Questions 1 through 6. 1. From the scatterplot and the value of r, we would describe the relationship between grams of carbohydrates and number of calories as having a direction that is and strength that is 2. Since we are attempting to use number of calories to predict grams of carbohydrates, we'd call number of calories a(n) variable and grams of carbohydrates a(n) variable.3. Consider the numbers 1.80 and 0.16 in the regression equation. We call the number 1.80 a(n) and the number 0.16 a(n) 4. How should we interpret the slope and intercept in the regression equation? In other words, what do these values tell us? Please share your thoughts below. A. Interpretation of the slope B. Interpretation of the intercept 5. Use the regression equation to predict the grams of carbohydrates for a beverage that has 285 w show your work in the space below. 6. The correlation between grams of carbohydrates and number of calories is r = 0.93. This means that % of the variability in grams of carbohydrates can be explained by the regression equation. It would also mean that % of the variability in grams of carbohydrates cannot be explained by the regression equation. Part 2: What is the wind speed of that hurricane? Hurricanes have been in the news lately, especially with the recent passing of Hurricane Ian. For years, scientists have studied the factors that affect the wind speed of hurricanes, and they have focused specifically on central pressure as one variable that is related to wind speed. It turns out that hurricanes develop low pressure at their centers. This leads to moist air being pulled in, and the moist air affects the rotation of the hurricanes. Ultimately, this rotation will generate high winds. Central pressure is measured in millibars and wind speed is measured in knots. The scatterplot below shows how these variables are related for a sample of 233 hurricanes. 150 125 Maximum Wind Speed (in knots) 100 75- 910 920 930 940 950 960 970 930 990 1000 Central Pressure (in mb) For this data set, the regression equation to predict the maximum wind speed of a hurricane based on central pressure is given below: Predicted maximum wind speed = 1028.1 - 0.97 (central pressure) Use the above information to answer Questions 7 through 10.7. Which one of the following statements is a correct interpretation of the regression equation? ? As central pressure goes up by one millibar, we predict maximum wind speed to increase by 1028.] knots. As central pressure goes up by one millibar, we predict maximum wind speed to increase by 0.97 knots. As central pressure goes up by one millibar, we predict maximum wind speed to decrease by 0.97 knots. . As central pressure goes up by one millibar, we predict maximum wind speed to decrease by 1028.1 knots. As central pressure goes down by one millibar, we predict maximum wind speed to decrease by 0.97 knots. cow .111 8. Use the regression equation to predict the wind speed of a hurricane that has a central pressure equal to 965 millibars. Show your work in the space below. 9. Would it be extrapolation to predict the wind speed of a hurricane that has a central pressure of 882 millibars? Please explain why or why not. 10. It turns out that for this data set, the percentage of variability in maximum wind speed that can be explained by the regression equation is equal to 81%. Put differently, this means that r2 = 81% (or 0.81). Given this information, we know the correlation between maximum wind speed and central pressure, or r, would need to equal