Biostats SDS 328M Homework 9 Part 1 - Hand work (all work must be done by hand). Write your answers onto one or more separate sheets of paper. Clearly mark each sheet with your name and your lab time. Round all answers to at least 3 decimal places and assume that =0.05 unless otherwise noted. 1. Cellular ability to regulate homeostasis is important for normal cell functioning and can be measured by basal calcium (Ca) pump activity (nmol/mg/hr). In a study investigating the effect of mercury (Hg) exposure in mothers on their newborn's cellular regulatory function, researchers measured the mercury deposits (mg/g) in the hair of a sample of 43 mothers along with their newborn's basal Ca pump activity. The data are summarized below: Mean St. Dev. Correlation Hair Hg Level (mg/g) 1,980.72 493.67 Basal Ca Pump Activity (nmol/mg/hr) 3,208.05 611.35 -0.51 a. Assuming all relevant assumptions were met, calculate the linear regression equation that predicts newborn basal Ca pump activity from maternal hair Hg level. (2pt) b. Within the context of the problem, interpret the estimates of the slope and intercept of the model. (1pt) c. What proportion of the variation in newborn basal Ca pump activity can be explained by the variation in maternal hair Hg level? (1pt) d. If a mother had a 2,500 mg/g mercury deposits in her hair, what would you predict her baby's basal Ca pump activity to be? (1pt) 2. Students in a lab grew a bacterium in broth culture at three different pH levels (acidic, neutral, basic) and across two temperatures (chilled, room temperature). Growth was measured by optical density (cells/mL). The mean densities for each combination of conditions are listed in the table below: Table 1 - Mean Bacterium Density (cells/mL) pH Acidic Neutral Basic Temperature Chilled Room Temp 11 16 12 23 14 21 Copyright 2016 Dept. of Statistics and Data Sciences, UT Austin a. Sketch an interaction plot displaying the mean density for each combination of temperature/pH levels. Plot pH on the horizontal axis and use different lines for the temperature levels. (2pt) b. From your graph, does there appear to be an interaction between temperature and pH on cell density? Why/why not? (1pt) c. Fill in the ANOVA table below. Use either p<0.05 or p>0.05 in the last column. (3pt) df pH Temperature pH* Temperature Error Total SS MS F p-value 216.5 330.8 423.7 45 2367.1 d. Write a full conclusion to this analysis. (3pt) Part 2 - R work (must be done in R) Copy and paste your R code and output into a word document to submit to Canvas. Follow these instructions to import the necessary dataset: Go to the Canvas Lab site and scroll down to the Lab 10 module. Click on \"Lab 10 Dataset,\" download lab10_bodyfat.csv, and save it to your computer. Remember: don't use Safari to download .csv files from Canvas. Import lab10_bodyfat.csv into R and name the data frame with your UT EID. Remember to include any code you use along with your answers in your submission! 3. This dataset contains information about the size (in cm) of different body parts of a sample of healthy adult men. You are interested in variables that can explain variation in abdomen size. a. Does thigh size have a significant linear relationship with abdomen size? Conduct the appropriate test and include all steps for full credit. (4pt) b. Compared to thigh size, is hip size a better linear predictor of abdomen size? Include the relevant statistics to support your answer. (2pt) Copyright 2016 Dept. of Statistics and Data Sciences, UT Austin