3. Fit a straight line trend using the method of least squares and estimate the profits for the year 1990. Year: 1981 1982 1983 1984 1985 1986 1987 Profits (Rs '000): 57 65 63 72 69 78 82
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- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.Calculate trend values by the method of least square from the data given below and estimate the sales for 1983 : Year 1976 1977 1978 1979 1980 : Sales of Co. ('000,000) : 70 74 80 86 90Below given are the figures of production (in thousand tonnes) of coal mine : Year 2002 2004 2005 2006 2007 2008 2011 Production ('000 tonnes) : () Fit a straight line trend by the method of least squares and calculate trend values. (i) What is the monthly increase in production of coal ? (ii) Eliminate the trend. 80 95 104 93 100 110 108
- Fit a straight linc trend by the method of least squares and estimate the production in 2015. 2006 2007 2008 2009 2010 2011 2012 Year: Production (in '000 tonnes): 80 90 92 83 94 99 92Fit the straight line trend to the following figures by the method of least squares: Year : 1975 1976 1977 1978 1979 1980 1981 Sales in *000 tonnes 50 60 65 63 68 70 72The percentage of adults in the labor force ages 65 and older who are still working has risen since 1990. The table below shows the data from 1990 to 2007. Let x represent the number of years after 1990. (a) Use the method of least squares to find the best line that fits these data. (b) Estimate the percent for the year 1991. (c) If the trend determined by the straight line in part (a) continues, when will the percent reach 16.8? Year 1990 1995 2000 2005 2007 % of Labor Force 11.4 12.1 13.3 13.9 15.1 (a) The line is y = X+ (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) (b) In the year 1991, the labor ce is predicted to 65 years old and older. (Use the answer from part a to find this answer. Round to the nearest tenth as needed.) (c) The percent will reach 16.8 in the year (Use the answer from part a to find this answer. Round to the nearest year as needed.)
- The percentage of adults in the labor force ages 65 and older who are still working has risen since 1990. The table below shows the data from 1990 to 2007. Let x represent the number of years after 1990. (a) Use the method of least squares to find the best line that fits these data. (b) Estimate the percent for the year 1991. (c) If the trend determined by the straight line in part (a) continues, when will the percent reach 16.8? Year 1990 1995 2000 2005 2007 % of Labor Force 11.4 12.1 13.3 13.9 15.1 (a) The line is y = x+ %3D (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) (b) In the year 19 the labor force is predicted to be 65 years old and older. (Use the answer from part a to find this answer. Round to the nearest tenth as needed.) (c) The percent will reach 16.8 in the year (Use the answer from part a to find this answer. Round to the nearest year as needed.)Fit a straight line trend bý the method of least squares to the following data and calculate trend valuęs : Year 1976 1977 1978 1979 1980 : Sales of T.V. Sets (in thousands) : 4 6. 7 8 10 Estimate the sales for the year 1985.vt 14. Calculate trend values by the method of Least Square from the data given below and estimate the sales for 2007. Year 2000 2001 2002 2003 2004 Sales of GA. (Rs. lakhs) 70 74 80 86 90 上
- The percentage of adults in the labor force ages 65 and older who are still working has risen since 1990. The table below shows the data from 1990 to 2007. Let x represent the number of years after 1990. (a) Use the method of least squares to find the best line that fits these data. (b) Estimate the percent for the year 1992. (c) If the trend determined by the straight line in part (a) continues, when will the percent reach 17.1? Year 1990 1995 2000 2005 2007 % of Labor Force 11 11.8 12.4 13.8 14.5 (a) The line is y= x+. %3D (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.)Calculate the trend values by the method of least squares. Also calculate the monthly increase in sales and trend value for 2012. Year 2001 2002 2003 2004 2005 2006 2007 Sales ($ Lakhs) 125 128 133 135 140 141 143A world wide fast food chain decided to carry out an experiment to assess the influence of income on number of visits to their restaurants or vice versa. A sample of households was asked about the number of times they visit a fast food restaurant (X) during last month as well as their monthly income (Y). The data presented in the following table are the sums and sum of squares. (use 2 digits after decimal point) ∑ Y = 393 ∑ Y2 = 21027 ∑ ( Y-Ybar )2 = SSY = 1720.88 ∑ X = 324 ∑ X2 = 14272 ∑ ( X-Xbar )2 = SSX = 1150 nx=8 ny=11 ∑ [ ( X-Xbar )( Y-Ybar) ] =SSXY=1090.5 PART A Sample mean income is Answer Sample standard deviation of income is Answer 90% confidence interval for the population mean income (hint: assume that income distributed normally with mean μ and variance σ2) is [Answer±Answer*Answer] 90% confidence interval for the population variance of income (hint: assume that income distributed normally with mean μ and variance σ2) is…
