Ivo Dinov
UCLA Statistics, Neurology, LONI

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STAT 13

Introduction to Statistical Methods for the Life and Health Science

Department of Statistics

Instructor: Ivo Dinov

Homework 7
Due Date: Friday, Mar. 12, 2010

Please, submit your homework before lecture on the due date. See the HW submission rules. On the front page include the following header.
• (HW_7) Do the following problems:
• In a study of protein synthesis in the oocyte (developing egg cell) of the frog Xenopus laevis, a biologist injected individual oocytes with radioactively labeled leucine. At various times after injection, he made radioactivity measurements and calculated how much of the leucine had been incorporated into protein. The results are given in the table below; each leucine value is the content of labeled leucine in two oocytes. All oocytes were from the same female. Assume time is measured in minutes after injection.

•  Index Time Leucine 1 0 0.02 2 10 0.25 3 20 0.54 4 30 0.69 5 40 1.07 6 50 1.50 7 60 1.74 Mean 30 0.83

• Use linear regression to estimate the rate of incorporation of the labeled leucine. Compare your results against the SOCR Regression Analysis applet.
• Plot the data and explain the regression line.
• Calculate by hand the residual standard deviation.
• Twenty plots, each 10 x 4 meters2 were randomly chosen in a large field of corn. For each plot, the plant density (number of plants in the plot) and the mean cob weight (grams of grain per cob) were observed. The results are given in the table below.
 Index Plant_Density_X Cob_Weight_Y 1 137 212 2 107 241 3 132 215 4 135 225 5 115 250 6 103 241 7 102 237 8 65 282 9 149 206 10 85 246 11 173 194 12 124 241 13 157 196 14 184 193 15 112 224 16 80 257 17 165 200 18 160 190 19 157 208 20 119 224 Mean 128.05 224.1

• Calculate the linear regression of Y on X using the SOCR Simple Linear Regression applet.
• Plot the data and draw the regression line on the graph.
• Interpret the values of the regression slope, intercept and correlation in the context of this setting.

• Use the SOCR Hot-dogs dataset to the effects of the type of meat on the sodium (first) and calorie (second) content of the hot-dogs. Use the SOCR 1-Way ANOVA applet to carry the calculations. Provide all results and explicitly state your inference.
• Use the SOCR 1981-2007 Consumer Price Index Dataset to explore the effect of the CPI item on the CPI-value, i.e., you can take the item as the categorical variable and the values as the observations (across months or/and years). Use the SOCR 1-Way ANOVA applet to carry the calculations. Provide all results and explicitly state your inference.

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