2 3 88% + HI 4 4. (13 points) A survey was conducted to find the association between price of pizza (per slice) and the volume of sales (in thousands of slices). The summary statistics is as given below: Variable Min Mean Median Max Standard Deviation Sale Volume (in thousands) 12.74 27.1 22.6 102 13.63 Sale Price (per slice in dollars) 2.05 2.85 2.87 3.4 0.28 The correlation is known to be -0.7. (a) (2 points) What percentage of variability in sale volume can be attributed to factors other than the price per slice of pizza? List 2 factors other than the price per slice that may affect the sale volume. (b) (6 points) Find the equation of the regression line. (c) (2 points) A sale price of $2.37 (per slice of pizza) is associated with a sale volume of 102,000 slices of pizza. Calculate the residual associated with this price point. (d) (3 points) A graph between residuals and price was plotted. What can you say about the adequacy of using linear regression to model the relationship between sale volume and price?STAT 1000: Homework 3 Deadline: 02/09/2022 at 11:59 pm 40 points 67 Instructions: . Give only necessary output from Minitab. You can copy and paste graphs on a Word document. . You need to show your work (formula setup, calculations, etc.) and state any properties or rules you need to solve the problems to get full credit. . Make sure to follow Gradescope guidelines while making a submission. A penalty of 1 point may be applied if the guidelines are not followed. 1. (4 points) A poultry scientist oversees a farm where there are two breeds of chickens. The eggs produced by those two breeds differ in size. The scientist has found that eggs from both breeds have normal distributions. The eggs from breed A have an average weight of 50 grams with a standard deviation of 3 grams. The eggs from breed B have an average weight of 63 grams with a standard deviation of 4. An egg was brought in for analysis but she did not know which breed the egg was from. The egg in question weighed 57 grams. Based on the weight, which breed is the egg more likely to have come from? 2. (4 points) Use the following dataset to answer the questions below. X 45 55 65 75 85 Y 30 50 70 50 30 (a) Make a scatterplot (using Minitab or by hand) of Y versus X and describe it. (b) Using Minitab, find the correlation between Y and X. (c) What important point about correlation does this exercise illustrate?2/3 88% + H Price [per slice) 5. (8 points) Use Minitab for questions (a) - (c) The percent of body fat is a matter of concern for health and fitness but the it is difficult and expensive to measure accurately. An attempt is being made to predict the body fat percentage using body measurements that are much easier to work with. The data is available in the Body Fat.xlax file. The variables used for this analysis are the body fat percentage, the body mass index (BMI), and the waist to hip ratio. Data for these variables is available in Column B (titled Pet.BF), Column Q (titled BMI). and column R (titled WHR) of the Body Fat.xlax file respectively. 3 (a) (2 points) Generate scatter plots with the fitted regression line and de them for simple linear regression taking: i. body fat percentage as response and BMI as explanatory variable. i. body fat percentage as response and WHR as explanatory variable. (b) (2 points) Give the simple linear regression equation between body fat percentage (Y) and BMI (X). Interpret the slope coefficient in context of the problem. (c) (2 points) Report the R-squared for: i. linear regression for body fat percentage and BMI. I. linear regression for body fat percentage and WHR.3 3 88% + (d) (1 point) Which of these two - BMI or WHR, in your opinion is a better predictor for body fat percentage? You may use the information from part (c) to answer this question. (e) (1 point) Find the predicted body fat percentage for a person with waist to hip ratio of 0.9 (by hand or Minitab). Note: Attempt after class on Friday, 02/04/22. 6. (8 points) A plant biologist is particularly interested in this species of wild mushroom with 4 different colors, white, brown, red, and purple, and their poisonous level. Throughout a few years, each time she collects a mushroom from this family, she takes it to the lab, tests for poison, and then records one entry into her database, with the color of the mushroom and whether it is poisonous or not (Yes/No). Below is a two-way table that summarizes the number of mushrooms she collected by two categorical variables: their color (White, Purple, Red, and Brown) and their poison (yes = poisonous or no = not poisonous). Based on this table, answer the following questions. Rows: Poison Columns: Color Brown Purple Red White b 120 167 634 1514 212 710 105 285 Court22.pdf "Dashboard My Pitt | All Campu... My Print Center ) Minitab 1 3 88% + H 3. (3 points) Make a scatterplot for the following data (using Minitab or by hand) X 1 2 3 4 10 10 Y 1 3 3 5 1 11 55 The correlation for this scatterplot is 0.5. What feature of the data is responsible for reducing the correlation to this value despite a strong straight-line association between X and Y in most of the observations