Ch. 3 ReviewAn



Ch. 3 ReviewAn agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian Pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years of the tree.predicted height=0.29+0.48(age)Which of the following is the best interpretation of the slope of the regression line?The height increases, on average, by 1 meter each 0.48 year.The height increases, on average, by 0.48 meter each year.The height increases, on average, by 0.29 meter each year.The height increases, on average, by 0.29 meter each 0.48 year.The difference between the actual height and the predicted height is, on average, 0.48 meter for each year.An experiment was conducted to investigate the relationship between the dose of a pain medication and the number of hours of pain relief. Twenty individuals with chronic pain were randomly assigned to one of the five doses – 0.0, 0.5, 1.0, 1.5, 2.0 – in milligrams (mg) of medication. The results are shown in the scatterplot below.The sum of the residuals is less than 0.The sum of the residuals is greater than 0.There are outliers associated with the lower doses.The variation in the hours of pain relief is not the same across the doses.There is a positive linear relationship between the residuals and the dose.A least-squares regression line was fitted to the weights (in pounds) versus age (in months) of a group of many young children. The equation of the line isy=16.6+0.65t,where y is the predicted weight and t is the age of the child. A 20-month-old child in this group has an actual weight of 25 pounds. Which of the following is the residual weight, in pounds for this child?-7.85-4.604.6057.85In a recent survey, 60 randomly selected married couples from the same town were asked to rate the overall quality of living in their town on a scale from 1 (very poor) to 10 (excellent) on twenty different attributes such as accessibility to major highways, availability of entertainment, services provided by tax dollars, etc. For each couple, the husband’s individual ratings on the twenty attributes were averaged to produce an overall quality rating, and the process was repeated for the wife. Each point on the scatterplot below displays the overall rating of one of the 60 couples with the husband’s rating represented by the horizontal axis and the wife’s rating represented by the vertical axis.Based on the scatterplot, which of the following statements is true? Husbands tended to rate the quality of living higher than their wives did.More overall ratings of 7 or less were assigned by husbands than by wives. The range in the husbands’ overall ratings is greater than the range in the wives’ overall ratings.The difference in overall ratings between a husband and wife was not more than 3 for any couple. For each couple, the overall rating assigned by the husband was the same as the overall rating assigned by the wife.In the scatterplot of y versus x shown below, the least squares regression line is superimposed on the plot. Which of the following points has the largest residual? ABCDEA student computed a least squares regression line and found that the correlation coefficient was 0.83. In checking her answer she found she had switched the explanatory and response variables. She then computed the regression line using the correct order. What is the new correlation coefficient?-10.83-0.830.6890.8310.83Which of the following scatterplots could represent a data set with a correlation coefficient of r = -1?A scatterplot of student height, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A.1485900-2540If the point labeled A is removed, which of the following statements would be true? The slope of the least squares regression line is unchanged and the correlation coefficient increases. The slope of the least squares regression line is unchanged and the correlation coefficient decreases. The slope of the least squares regression line increases and the correlation coefficient increases. The slope of the least squares regression line increases and the correlation coefficient decreases. The slope of the least squares regression line decreases and the correlation coefficient increases. The computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river.1485900102235Which of the following statements is a correct interpretation of the value 19.0 in the output?On average there is a predicted increase of 19.0 ppm in concentration of lead for every increase of 1 ppm in concentration of zinc found in the fish.On average there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish.The predicted concentration of zinc is 19.0 ppm in fish with no concentration of lead.The predicted concentration of lead is 19.0 ppm in fish with no concentration of zinc.Approximately 19% of the variability in zinc concentration is predicted by its linear relationship with lead concentration.The weight, in pounds, of a full backpack and the corresponding number of books in the backpack were recorded for each of 10 college students. The resulting data were used to create the residual plot and the regression output shown below.114300035560Which of the following values is closest to the actual weight, in pounds, of the backpack for the student who had 4 books in the backpack?810131517 Researchers studying a pack of gray wolves in North America collected data on the length x, in meters from nose to tip of tail, and the weight y, in kilograms, of the wolves. A scatterplot of weight versus length revealed a relationship between the two variables described as positive, linear, and strong.For the situation described above, explain what is meant by each of the following words.Positive:Linear:Strong:The data collected from the wolves were used to create the least-squares equationy =-16.46+35.02x.Interpret the meaning of the slope of the least-squares regression line in context.One wolf in the pack with a length of 1.4 meters had a residual of -9.67 kilograms. What was the weight of the wolf?A student measured the heights and the arm spans, rounded to the nearest inch, of each person in a random sample of 12 seniors at a high school. A scatterplot of arm span versus height for the 12 seniors is shown.Based on the scatterplot, describe the relationship between arm span and height for the sample of 12 seniors.Let x represent height, in inches, and let y represent arm span, in inches. Two scatterplots of the same data are shown below. Graph 1 shows the data with the least squares regression line y=11.74+0.8247x, and graph 2 shows the data with the line y= x.The criteria described in the table below can be used to classify people into one of three body shape categories: square, tall rectangle, or short rectangle.(i)For which graph, 1 or 2, is the line helpful in classifying a student’s body shape as square, tall rectangle, or short rectangle? Explain.(ii)Complete the table of classifications for the 12 seniors.(c) Using the best model for prediction, calculate the predicted arm span for a senior with height 61 inches. ................
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