The Honeybee Waggle Dance When honeybee scouts find a food source or a nice site for a new home, they communicate the location to the rest of the swarm by doing a "waggle dance." They point in the direction of the site and dance longer for sites farther away. The rest of the bees use the duration of the dance to predict distance to the site. Table 1 shows the distance, in meters, and the duration of the dance, in seconds, for seven honeybee scouts.2 Duration Distance 0.40 200 0.45 250 0.95 500 1.30 950 2.00 1950 3.10 3500 4.10 4300 Table 1 Duration of a honeybee waggle dance to indicate distance to the source Check out a honeybee waggle dance on youtube! 2Seeley, T., Honeybee Democracy, Princeton University Press, Princeton, NJ, 2010, p. 128. (a) Which is the response variable? O Distance O Duration(b) Figure 1 shows a scatterplot of the data. 4000 3000 Distance 2000- 1000 - 3 Duration Figure 1 Using dance duration to predict distance to source Does there appear to be a linear trend in the data? If so, is it positive or negative? O No, there appears to be no linear trend in the data. Yes, there appears to be a positive linear trend in the data. O Yes, there appears to be a negative linear trend in the data. eTextbook and Media Hint (c) Use technology to find the correlation between the two variables. Round your answer to three decimal places.(d) Use technology to find the regression line to predict distance from duration. Round your answers to the nearest integer. Distance = i i Duration) e Textbook and Media Hint (e) Interpret the slope of the line in context. O The slope tells the expected change in distance if the duration is 1 second more. O The slope tells the expected distance if the duration is 1 second more. O The slope tells the expected change in duration if the distance is 1 meter more. O The slope tells the expected duration if the distance is 1 meter more. e Textbook and Media Hint (f) Round your answers to the nearest integer. Predict the distance to the site if a honeybee does a waggle dance lasting 1 second. distance after 1 second = i meters Predict the distance to the site if a honeybee does a waggle dance lasting 3 seconds. distance after 3 seconds = metersThe Impact of Strong Economic Growth In 2011, the Congressional Budget Office predicted that the US economy would grow by 2.8 % per year on average over the decade from 2011 to 2021. At this rate, in 2021, the ratio of national debt to GDP (gross domestic product) is predicted to be 76 % and the federal deficit is predicted to be $861 billion. Both predictions depend heavily on the growth rate. If the growth rate is 3.3 % over the same decade, for example, the predicted 2021 debt-to-GDP ratio is 66 % and the predicted 2021 deficit is $521 billion. If the growth rate is even stronger, at 3.9 % , the predicted 2021 debt-to-GDP ratio is 55 % and the predicted 2021 deficit is $1 13 billion. There are only three individual cases given (for three different economic scenarios), and for each we are given values of three variables. Click here to access StatKey. 1Gandel, S., "Higher growth could mean our debt worries are all for nothing," Time Magazine, March 7, 2011, p. 20. (a) Use Statkey or other technology and the three cases given to find the regression line for predicting 2021 debt-to-GDP ratio (in percents) from the average growth rate (in percents) over the decade 2011 to 2021. Round your answer for the intercept to the nearest integer and your answer for the slope to one decimal place. Ratio = i (Growth) eTextbook and Media Hint (b) Round your answers to one decimal place. What 2021 debt-to-GDP ratio does the model in part (a) predict if growth is 2 % ? Ratio = i % What 2021 debt-to-GDP ratio does the model in part (a) predict if growth is 4 % ? Ratio = i %(c) Studies indicate that a country's economic growth slows if the debt-to-GDP ratio hits 90 % . Using the model from part (a), at what growth rate would we expect the ratio in the US to hit 90 % in 2021? Round your answer to two decimal places. growth = i % eTextbook and Media Hint (d) Use Statkey or other technology and the three cases given to find the regression line for predicting the deficit (in billions of dollars) in 2021 from the average growth rate (in percents) over the decade 2011 to 2021. Round your answers to the nearest integer. Deficit = i i (Growth) eTextbook and Media Hint (e) Round your answers to the nearest integer. What 2021 deficit does the model in part (d) predict if growth is 2 % ? Deficit = i billion dollars What 2021 deficit does the model in part (d) predict if growth is 4 % ? Deficit = i billion dollars(f) The deficit in 2011 was $1.4 trillion. What growth rate would leave the deficit at this level in 2021? Round your answer to three decimal places. Growth = i %Height and Weight Using the data in the StudentSurvey dataset containing the students' weight and height, we use technology to find that a regression line to predict weight (in pounds) from height (in inches) is Weight = - 170 + 4.82 (Height). Click here for the dataset associated with this question. (a) What weight does the line predict for a person who is 5 feet tall (60 inches)? Round your answer to one decimal place. Weight = i pounds What weight is predicted for someone 6 feet tall (72 inches)? Round your answer to two decimal places. Weight = i pounds eTextbook and Media Hint (b) What is the slope of the line? Round your answer to two decimal places. Slope = i Interpret it in context. The slope gives{c} Does the intercept make sense in this context? 0 Yes O No eTextbook and Media Hint {d} What weight does the regression line predict For a baby who is 20 inches long? Round your answer to one decimal place. Weight = n pounds Why is it not appropriate to use the regression line in this case? It is because v . Find a 95 % confidence interval for the slope of the model below with n = 24. The regression equation is Y = 86.1 - 7X. Predictor Coef SE Coef T P Constant 86.135 4.370 19.71 0.000 X -7.0017 0.8170 -8.57 0.000 Round your answers to two decimal places. to