For certain data the following regression equations were obtained: 4х — 5у + 33 % 0 20x + 9y -- 107 = 0 Estimate y when x = 20 and x when y = 20
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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?bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
- .The worker has noticed that the more time he spends at work (x), the less money he is likely to make (y) in conducting transactions for his firm. Which of the regression equations MOST suggests such a possibility?A set of X and Y scores has MX = 4, SSX = 10, MY = 5, SSY = 40, and SP = 20. Which is the regression equation for predicting Y from X?A carpenter wanted to predict how many pieces of furniture they could produce in a certain time frame. They calculated a linear regression equation and obtained the following results:Using these results how many pieces can they create in 5 hours? y^=2x+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 _____.Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2The admissions officer for a certain college developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high school GPA. ŷ = −1.39 + 0.0234x1 + 0.00482x2 where x1 = high-school grade point average x2 = SAT mathematics score y = final college grade point average. #1)A high-school average 84 corresponds to x1 = 84 and a score of 535 on the SAT mathematics test corresponds to x2 = 535. Substitute these values into the estimated regression equation to find the final college GPA, rounding the result to two decimal places. GPA = −1.39 + 0.0234x1 + 0.00482x2 = -1.39 +0.0234 (_____________) + 0.00482 (535) = __________________
- Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 3 8 6 10 13 (d) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. ŷ = (e) Use the estimated regression equation to predict the value of y when x = 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 multiple coefficient of determination is _____.A set of X and Y scores has Mx=4, SSx=10, My=5, SSy = 40, and SP=20. What is the regression equation for predicting Y from X?