An architect wants to determine the relationship between the heights (in feet) of a building and the number of floors in the building. The data for a sample of 10 buildings in Pittsburgh are shown. Number of Floors, x | 64 | 54 | 40 | 31 | 45 | 38 | 42 | 41 | 37 | 70 Height, y | 751 | 725 | 635 | 616 | 654 | 643 | 635 | 620 | 611 | 701 Use these data for exercises 11–16. 11. (2 points) Find the equation of the least squares regression line for data. 12. (1 point) Describe the slope in context. 13. (1 point) What is the correlation coefficient? 14. (1 point) Find the explained variance R^2. 15. (2 points) Estimate the height of a building that has 57 floors. 16. (2 points) Calculate the residual for the observation (54, 725).
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Perform the following steps. a. Draw the scatter plot for the variables. b. Compute the value of the correlation coefficient. c. State the hypotheses. d. Test the significance of the correlation coefficient at $\alpha=0.05,$ using Table I. e. Give a brief explanation of the type of relationship. Assume all assumptions have been met. An architect wants to determine the relationship between the heights (in feet) of buildings and the number of stories in the buildings. The data for a sample of 10 buildings in Chicago are shown. Explain the relationship (if any). $$ \begin{array}{l|cccccccccc} \text { Stories } x & 64 & 68 & 50 & 48 & 32 & 46 & 58 & 45 & 49 & 40 \\ \hline \text { Height } y & 995 & 844 & 732 & 679 & 648 & 635 & 610 & 600 & 583 & 573 \end{array} $$
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The table below shows the heights (in feet) and the number of stories of six notable buildings in a city. Height, x: 772, 628, 518, 508, 496, 483 Stories, y: 51, 48, 44, 43, 39, 37 You want to build a linear model that will predict the number of stories in a building from the height of the building. a) Using your calculator, find the equation of the regression line in statistical form for the given data. b) Use the regression equation to predict the number of stories for a building that is 640 feet tall. y = ( ) + ( )x (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) (b) Predict the number of stories in a building that is 640 feet tall. Choose the correct answer below. A. 34 B. 47 C. 41 D. not meaningful
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