MAT 114 QUANTITATIVE REASONING SPRING 2016 PROJECT TWO The objective of this project is to use a spreadsheet program to test correlation strength and to create and utilize mathematical functions which model relationships between pairs of quantities, especially relationships which demonstrate linear or exponential growth/decay. Important definitions and helpful examples related to this project are provided in Chapter 3 of the NAU MAT 114 course website. Specifically: 3A - independent/dependent variables, positive/negative correlation, correlation coefficient 3B - comparing linear and exponential growth/decay 3E - implementing functions using Microsoft Excel (video example) A spreadsheet file containing the data sets required for this project must be downloaded from the NAU MAT 114 course website. All required charts/graphs must be created within a spreadsheet program. Handwritten or handdrawn charts/graphs will not be accepted. Answers to the following questions must be compiled into a single word-processing document (Microsoft Word, etc.), including necessary explanatory text and supporting charts/graphs. Explanations and discussions of answers must be in complete, grammatically correct sentences. The final document must be neat and organized, with answers to individual problems clearly labeled. The method of submission of the final document (i.e. printed out, submitted electronically, etc.) will be determined by individual instructors. This project must be submitted at the start of your Class Meeting during Week 10 of this semester. EAGLES A study was conducted on Admiralty Island in southeast Alaska using time-lapse photography to document Bald Eagle incubation, brooding (sitting on eggs to hatch them), prey deliveries and feeding. It provides a number of insights into male/female role differentiation including how roles and behaviors change based on environmental factors. While both male and female Bald Eagles brood, for example, the percentage of time the female broods during a given day appears to depend on several aspects of that day's weather. 1. Data in the accompanying spreadsheet documents 19 days during the above study. For each day, the percentage of that day which was considered by scientists to be \"sunny\" was measured along with the percentage of that day during which the female Bald Eagle brooded (that is, sat on her eggs). a) Does it appear these quantities are positively related or negatively related? Why, do you think, these quantities would be related in this way? b) Create a scatterplot of the data. (This is accomplished in Microsoft Excel by highlighting all of the data, clicking the \"Insert\" tab, and selecting \"Scatter\".) c) Have your spreadsheet program create a linear regression trendline for the data, displaying the equation and the coefficient of determination (R2) on the graph. (This is accomplished in Microsoft Excel by right-clicking on a data point in your scatterplot, selecting \"Add Trendline...\Percent of Day Sunny Percent Female Brooding Time 0.2 81.1 1.3 68.5 1.6 59.8 6.8 70.1 8.1 69.3 11.2 57.0 17.4 64.4 18.6 62.2 37.2 67.4 38.1 51.5 40.2 68.2 44.2 45.8 44.3 39.1 46.1 60.8 52.9 59.7 54.6 57.9 55.1 42.6 70.9 37.0 80.4 44.1 Advertising Print Month Sales Clothing (General) Online Clothing (Technical) Shoes Accessories Skateboard Equipment Snowboard Equipment Mar. 2008 $ 745.37 $ - $ 40,995.35 $ 13,840.26 $ 37,466.50 $ 27,417.81 $ 18,757.31 $ 41,520.79 May 2008 $ 225.90 $ - $ 9,713.70 $ 4,351.46 $ 41,191.23 $ 7,032.58 $ 40,007.60 $ 21,757.31 Jul. 2008 $ 225.90 $ - $ 8,584.20 $ 3,326.22 $ 45,164.17 $ 5,955.21 $ 41,520.79 $ 19,957.31 Sep. 2008 $ 556.31 $ 150.00 $ 22,252.40 $ 9,828.66 $ 61,187.37 $ 17,137.40 $ 29,310.75 $ 17,557.31 Nov. 2008 $ 225.90 $ 150.00 $ 11,295.00 $ 10,879.25 $ 34,197.31 $ 12,184.00 $ 28,614.90 $ 33,916.98 Jan. 2009 $ 647.47 $ 210.00 $ 24,603.86 $ 9,488.96 $ 46,159.32 $ 18,582.04 $ 19,541.74 $ 49,373.77 Mar. 2009 $ 225.90 $ 150.00 $ 8,810.10 $ 7,593.40 $ 38,460.50 $ 9,298.62 $ 17,319.38 $ 34,216.98 May 2009 $ 225.90 $ 370.00 $ 11,746.80 $ 6,656.56 $ 42,251.23 $ 11,907.31 $ 40,007.60 $ 15,519.38 Jul. 2009 $ 225.90 $ 370.00 $ 11,520.90 $ 9,799.85 $ 45,927.17 $ 13,366.00 $ 42,958.72 $ 15,519.38 Sep. 2009 $ 634.41 $ 370.00 $ 27,914.04 $ 8,736.56 $ 60,972.37 $ 21,030.93 $ 30,748.68 $ 19,119.38 Nov. 2009 $ 556.10 $ 411.27 $ 26,136.70 $ 16,779.82 $ 34,147.31 $ 24,465.67 $ 29,094.21 $ 71,560.98 Jan. 2010 $ 816.13 $ 514.17 $ 39,990.37 $ 17,207.72 $ 45,669.32 $ 32,358.91 $ 20,979.67 $ 81,651.19 Mar. 2010 $ 225.90 $ 370.00 $ 9,939.60 $ 24,060.47 $ 38,254.50 $ 19,705.66 $ 17,798.69 $ 77,001.89 May 2010 $ 225.90 $ 568.30 $ 8,358.30 $ 13,382.35 $ 42,607.23 $ 15,026.02 $ 39,528.29 $ 15,398.69 Jul. 2010 $ 615.10 $ 511.63 $ 22,758.70 $ 13,007.35 $ 46,731.17 $ 21,624.32 $ 44,396.65 $ 15,998.69 Sep. 2010 $ 615.10 $ 455.21 $ 30,755.00 $ 10,540.21 $ 61,131.37 $ 23,976.33 $ 31,707.30 $ 16,598.69 Nov. 2010 $ 472.38 $ 723.16 $ 22,674.24 $ 9,145.10 $ 34,190.31 $ 21,197.78 $ 28,135.59 $ 81,247.31 Jan. 2011 $ 823.61 $ 973.24 $ 34,591.62 $ 20,838.83 $ 46,161.32 $ 34,832.04 $ 22,417.60 $ 84,156.90 Mar. 2011 $ 745.37 $ 479.26 $ 27,578.69 $ 21,082.77 $ 38,241.50 $ 27,835.32 $ 18,278.00 $ 74,261.94 May 2011 $ 225.90 $ 479.26 $ 8,584.20 $ 5,521.89 $ 43,027.23 $ 10,557.64 $ 39,528.29 $ 15,878.00 Jul. 2011 $ 410.00 $ 419.96 $ 17,630.00 $ 11,378.78 $ 47,110.17 $ 17,575.35 $ 45,834.58 $ 15,278.00 Sep. 2011 $ 556.31 $ 706.23 $ 22,252.40 $ 14,746.01 $ 61,782.37 $ 23,663.51 $ 33,624.54 $ 20,678.00 Nov. 2011 $ 410.00 $ 513.13 $ 16,810.00 $ 23,732.94 $ 33,711.31 $ 24,023.73 $ 29,094.21 $ 68,120.05 Jan. 2012 $ 823.61 $ 885.24 $ 42,004.11 $ 41,757.47 $ 46,390.32 $ 48,354.11 $ 21,458.98 $ 80,125.16 Mar. 2012 $ 410.00 $ 515.00 $ 18,450.00 $ 14,484.84 $ 38,024.50 $ 20,233.36 $ 18,278.00 $ 71,459.06 May 2012 $ 485.37 $ 398.67 $ 18,444.06 $ 11,531.02 $ 42,714.23 $ 17,902.81 $ 40,966.22 $ 18,278.00 Jul. 2012 $ 450.19 $ 445.23 $ 20,708.74 $ 7,086.11 $ 48,025.17 $ 17,153.17 $ 46,313.89 $ 15,878.00 Sep. 2012 $ 601.32 $ 851.20 $ 25,255.44 $ 10,748.67 $ 62,695.37 $ 24,226.45 $ 32,665.92 $ 19,478.00 Nov. 2012 $ 450.19 $ 478.40 $ 23,409.88 $ 28,177.48 $ 34,695.31 $ 29,291.98 $ 27,656.28 $ 67,310.05 Jan. 2013 $ 837.95 $ 1,003.21 $ 37,707.75 $ 41,927.54 $ 47,061.32 $ 47,153.62 $ 20,021.05 $ 80,638.16 Mar. 2013 $ 450.19 $ 512.70 $ 18,907.98 $ 13,878.81 $ 39,095.50 $ 20,142.51 $ 18,278.00 $ 70,968.06 May 2013 $ 510.40 $ 461.61 $ 22,968.00 $ 12,664.62 $ 42,831.23 $ 21,191.83 $ 40,007.60 $ 19,269.00 Jul. 2013 $ 660.71 $ 491.15 $ 25,106.98 $ 11,401.87 $ 48,731.17 $ 21,845.96 $ 46,793.20 $ 15,367.00 Sep. 2013 $ 715.25 $ 655.15 $ 31,471.00 $ 7,778.30 $ 62,781.37 $ 24,415.43 $ 31,707.30 $ 19,404.00 Nov. 2013 $ 455.37 $ 497.35 $ 23,679.24 $ 18,549.26 $ 34,546.31 $ 24,751.12 $ 28,614.90 $ 66,534.05 Jan. 2014 $ 845.61 $ 1,115.51 $ 32,133.18 $ 32,595.20 $ 47,093.32 $ 40,521.36 $ 21,458.98 $ 81,789.16 Mar. 2014 $ 455.39 $ 364.85 $ 18,670.99 $ 17,414.43 $ 39,565.50 $ 20,710.67 $ 19,236.62 $ 71,650.06 May 2014 $ 455.39 $ 497.10 $ 22,769.50 $ 9,554.80 $ 43,433.23 $ 19,797.19 $ 40,007.60 $ 18,555.00 Jul. 2014 $ 710.15 $ 497.10 $ 36,217.65 $ 14,876.90 $ 48,481.17 $ 29,182.32 $ 47,751.82 $ 15,835.00 Sep. 2014 $ 710.15 $ 864.13 $ 26,275.55 $ 23,461.58 $ 63,152.37 $ 31,187.52 $ 33,145.23 $ 19,271.00 Nov. 2014 $ 517.36 $ 495.31 $ 20,177.04 $ 16,980.18 $ 34,985.31 $ 22,200.56 $ 28,614.90 $ 67,565.05