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Name: _________________________________________________________________________ Period: _____________Chapter 3 Practice FRQ1.?A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay under water.31?For all but the shallowest dives,?there is a linear relationship that is different for different penguins.?The study gives a scatterplot for one penguin titled “The Relation of Dive Duration?(y)?to Depth(x).” Duration?y?is measured in minutes and depth?x?is in meters.?The report then says,“The regression equation for this bird is:??= 2.69 + 0.0138x.”(a)?What is the slope of the regression line??Interpret this value(b)?Does the?y?intercept of the regression line make any sense??If so,?interpret it.?If not,?explain why not(c)?According to the regression line,?how long does a typical dive to a depth of 200 meters last?(d)?Suppose that the researchers reversed the variables,?using?x?= dive duration and?y?= depth.?What effect will this have on the correlation??On the equation of the least-squares regression line?2.?In Professor Friedman’s economics course,?the correlation between the students’ total scores prior to the final examination and their final-examination scores is?r?= 0.6.?The pre-exam totals for all students in the course have mean 280 and standard deviation 30.?The final-exam scores have mean 75 and standard deviation 8.?Professor Friedman has lost Julie’s final exam but knows that her total before the exam was 300.?He decides to predict her final-exam score from her pre-exam total.(a)?Find the equation for the appropriate least-squares regression line for Professor Friedman’s prediction.(b)?Use the least-squares regression line to predict Julie’s final-exam score.(d)?Julie doesn’t think this method accurately predicts how well she did on the final exam.?Determine r2.?Use this result to argue that her actual score could have been much higher?(or much lower)?than the predicted value. 516256211455003. Sarah’s parents are concerned that she seems short for her age.?Their doctor has the following record of Sarah’s height:(a)?Make a scatterplot of these data.(b)?Using your calculator,?find the equation of the least-squares regression line of height on age.(c)?Use your regression line to predict Sarah’s height at age 40 years?(480 months).?Convert your prediction to inches?(2.54 cm = 1 inch).(d)?The prediction is impossibly large.?Explain why this happened.3678555837565004. ?Drilling down beneath a lake in Alaska yields chemical evidence of past changes in climate.?Biological silicon,?left by the skeletons of single-celled creatures called diatoms,?is a measure of the abundance of life in the lake.?A rather complex variable based on the ratio of certain isotopes relative to ocean water gives an indirect measure of moisture,?mostly from snow.?As we drill down,?we look further into the past.?Here is a scatterplot of data from 2300 to 12,000 years ago:(a)?Identify the unusual point in the scatterplot.?Explain what’s unusual about this point.(b)?If this point was removed,?describe the effect oni.?the correlation.ii.?the slope of the least-squares line. ................
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