The heights of a sample of 10 fathers and their eldest sons are given below : Height of fathers (X) Height of son (Y) 170 167 162 193 167 166 169 171 164 165 168 167 166 166 168 165 168 170 165 168 (i) Compute the regression of Y on X. (ii) Compute the correlation coefficient. (iii) Compute the coefficient of determination and give your comments.
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- Data on pollution and cost of medical care for elderly people are given in the following table. Region Pollution Cost of Medical Care North 30.0 915 Upper South 31.8 891 Deep South 32.1 968 West South 26.8 972 Big Sky 30.4 952 West 40.0 899 Compute the regression line and determine the residuals Compute the correlation coefficient. Does the value of r indicate that the linear relationship is strong? Are there any unusual feature of the residual plot?For the data given in the table below, find the linear correlation coefficient r and the least-squares regression line x y ------- 1 18 3 13 3 9 6 6 7 4 -------A random sample of nonindustrialized countries was selected, and the life expectancy in years is listed for both men and women. Men 61.7 42.8 72.6 57.9 55.4 62.1 Women 50.4 74.2 75.3 75.4 49.1 65.2 The correlation coefficient for the data is =r−0.003 and =α0.05. Should regression analysis be done? Now Find the equation of the regression line. Round the coefficients to at least three decimal places. =y′+abx =a =b Now Find women's life expectancy in a country where men's life expectancy =60 years. Round your answer to at least three decimal places. Women's life expectancy is ____ years.
- The ages (X) of ten second-hand cars and their km values (Y) are given below.a) Calculate the correlation coefficient between X and Y.b) Calculate the coefficients of the regression line of the Y with respect to X.c) Estimate the km value of a 5.0 year old car. X and Y values given in the picture.The average gasoline price per gallon (in cities) and the cost of a barrel of oil are shown below for a random selection of weeks in 2015 . Oil ( $ ) Gasoline ( $ ) 47.79 2.638 44.62 2.636 81.08 2.944 43.67 2.528 40.58 2.623 48.64 2.682 The correlation coefficient for the data is =r0.954 and =α0.01. Should regression analysis be done? Find the equation of the regression line. Round the coefficients to at least three decimal places. =y′+abx =a =b Find the cost of gasoline when oil is $57 a barrel. Round the answer to at least three decimal places. When oil is $57 a barrel, gas costs $ per gallon.A study of the amount of rainfall and the quantity of air pollution removed produced the following data shown in table below: Daily Rainfall x (0.01 cm) Particulate Removed y (μg/m3) 7 126 7.9 129.3 7.5 125.3 9.2 120.2 10.8 116.7 5.8 119.2 5.6 138.7 2.7 147.5 9.2 110.3 Compute and interpret the coefficient of determination, and coefficient of correlation for the given data. What will be the regression equation, when swapped depended and independent variable
- The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1xy^=b0+b1x. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.01 level of significance. Critical Values of the Pearson Correlation Coefficient Average Temperatures and Snow Accumulations Average Temperature (℉℉) 42 27 22 39 44 21 27 18 32 36 Snow Accumulation (in.in.) 6 11 22 8 12 27 27 20 12 6 Regression equation y=_______________ Is the equation appropriate?4.For a sample of 12 observations, a businessman wants to regress the price (in dollar) of the laptop (Y) on the processor's speed (X). The summary results of the observations are given below. Σx = 19.8 , Σy = 24798, Σxy = 431882 Σx^2 = 33.88, Σγ^2 = 57365692 (b)Find the fitted regression line of the price of laptop on processor speed. (c) Find the predicted price of the laptop (y) for the processor speed x-1.9. (d) Compute the coefficient of determination and comment.The following table shows the number of full-time faculty that WVU has on staff throughout the years.Year # of Faculty2003 12102007 13302009 14202013 14702017 15002018 1660 (A) Find the equation of the regression line that represents the number of full-time faculty, F , as a function of x years since 2000. (round the regression coefficients to two decimal places)F(x) =_______________________? (B) What is the correlation coefficient (r-value) for the regression model? (Round your answer to three decimal places)r =________? (C) Given the value of r , does the regression line model the data well? That is, does the equation do a good job of modeling the data? 1.)No, the r-value is high, meaning the data can't be modeled using a line2.)Yes, the r-value is low, meaning the data can be modeled using a line 3.)No, the r-value is low, meaning the data can't be modeled using a line4.)Yes, the r-value is high, meaning the data can be modeled using a line Answer______________? (D) Using the…
- Listed below are costs (in dollars) of air-fares for different airlines from New York City to San Francisco. The costs are base on tickets purchased 30 days in advance and on day in advance. 30 days x 240 250 254 284 288 328 290 One day y 556 514 587 843 728 988 536 Compute the correlation coefficient. Compute the slope of the linear regression line. Compute the y-intercept of the linear regression Use the equation of the regression line(and parts b. and c.) to give a point estimate of the cost of a ticket purchased one day in advance, given the ticket cost of $310 if purchased 30 days in advance of the flight. Give a 95% confidence interval for y when x is $310.The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1x. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.01 level of significance. Critical Values of the Pearson Correlation Coefficient Average Temperatures and Snow Accumulations Average Temperature (℉) 42 27 22 39 44 21 27 18 32 36 Snow Accumulation (in.) 6 11 22 8 12 27 27 20 12 61. Plot the data points on a scatter diagram. 2. Determine the equation of the regression line and find Pearson product-moment correlation coefficient. 3. Determine the point estimate of y at x = 5.5