Example 17.8 Find the multiple linear regression of X, on X2 and X3 from the data relating to three variables given below: X; : X2: X3 : 10 38 25 29 16 14 12 39 20 31 16 23 10 23 16 13 11
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- The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.
- The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The multiple coefficient of determination is _____.Consider the following correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. For each give the fraction of the variation in y that is explained by the least-squares regression of y on x.he following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a)With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =
- The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 70 30 1995 130 40 110 40 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = (b) Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) =The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 120 40 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a)With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) =
- A study of law firms produced the following regression output. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 7.443 2.990 2.489 0.010 x1 0.214 0.044 4.864 0.000 x2 -1.143 0.581 -1.967 0.028 x3 -0.159 0.057 -2.789 0.114 x4 0.579 0.314 1.844 0.001 x5 -0.024 0.021 -1.143 0.112 ANOVA Table Source DF SS MS F P-Value Regression 5 1975.76 395.2 9.68 0.000 Residual Error 55 2244.25 40.80 Total 60 4220.01 How large is the sample? Compute the F statistic (round to 2 decimal places) State the Decision Rule for each independent variable. Use the 0.05 significance level. Reject Ho if t<? or t>? (round to 3 decimal places).The birth lengths in cm (x) and birth weights in kg (y) of a sample of 50 newborn female babies are compared, yielding a correlation coefficient of r=0.578 and a linear regression equation of ŷ =−8.89+0.243x The babies all had lengths between 46.5 and 53.0 cm, and weights between 2.50 and 4.05 kg. Based on this, predict the birth weight of a newborn female baby with a birth length of 48.5 cm.The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 120 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Graph the associated points and regression line. (b) What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of education doctorates for each additional social science doctorate.The slope tells us the decrease in the number of education doctorates for each additional social science doctorate. The slope tells us the increase in the number…