The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x,1 - 2.3x2 + 7.6x3 + 2.7x4 %3D | The values of SST and SSR are 1,804 and 1,779, respectively. (a) Compute R?. (b) Compute R,. (c) Comment on the goodness of fit.
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A: Givensum of squares of Residuals(SSR)=600sum of squared estimated of errors(SSE)=200
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A: Given: n=5, ∑x=15, ∑y=20, ∑x-x2=10, ∑y-y2=26 and ∑x-xy-y=13. Then,x=∑xn=155=3y=∑yn=205=4
Q: The following estimated regression equation is based on 30 observations. ŷ = 18.3 + 3.9x1 − 2.2x2 +…
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Q: The following estimated regression equation is based on 30 observations. ŷ = 18.5 +4x1- 2.4x2 +…
A: From the provided information, Number of observations (n) = 30 Number of independent variable (k) =…
Q: In a regression model involving 30 observations, the following estimated regression equation was…
A: Given SSR = 1,740 SST = 2,000. N=number of observation=30, K=Number of explanatory variables…
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A: given n = 30 observation y⏞ =17.2 +3.6 x1 - 2.2x2 + 7.8 x3 -2.9x4 The values of SST and SSR are…
Q: he following estimated regression equation is based on 10 observations was presented. ere SST…
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Q: The following estimated regression equation is based on 30 observations. ŷ = 18.5 + 3.7x1 – 2.2x2 +…
A: Solution
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Q: The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x,…
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Q: The following estimated regression equation based on 10 observations was presented. 9 = 29.1240 +…
A: From the provided information, SST = 6721.125 and SSR = 6215.375 b) The required value of R2 can be…
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Q: The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x1…
A: (a) The values of SST and SSR are 1,807 and 1,757, respectively. The value of R2 is,…
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Q: In a regression analysis involving 27 observations, the following estimated regressionequation was…
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Q: 4. Consider the following multiple regression results, where the dependent variable is the number of…
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Q: regression model involving 30 observations, the following estimated regression equation was…
A: Given that The regression equation was obtained.ŷ = 170 + 34x1 – 3x2 + 8x3 + 58x4 + 3x5 SSR = 1740…
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A: a. The coefficient of determination is, R2=1-SSRSST=1-17551803=1-0.973=0.027 Thus, the value of R2…
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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 equation based on 30 observations was presented. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,808 and 1,780, respectively. (a) Compute R2. (b) Compute Ra2. (c) Comment on the goodness of fit.
- In a regression analysis involving 27 observations, the following estimated regressionequation was developed:yˆ 5 25.2 1 5.5x1For this estimated regression equation SST = 1550 and SSE = 520.a. At a = .05, test whether x1 is significant.Suppose that variables x2 and x3 are added to the model and the following regressionequation is obtained.yˆ 5 16.3 1 2.3x1 1 12.1x2 2 5.8x3For this estimated regression equation SST = 1550 and SSE = 100.The following estimated regression equation is based on 30 observations. ŷ = 18.3 + 3.9x1 − 2.2x2 + 7.5x3 + 2.5x4 The values of SST and SSR are 1,805 and 1,762, respectively. a. Compute R2 = (to 3 decimals). b. Compute Ra2 = (to 3 decimals).The 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) = __________________
- The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,807 and 1,757, respectively. (a) Compute R2. (Round your answer to three decimal places.) R2 = (b) Compute Ra2. (Round your answer to three decimal places.) Ra2 = (c) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The estimated regression equation did not provide a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation provided a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation did not provide a good…The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,801 and 1,758, respectively. (a)Compute R2. (Round your answer to three decimal places.) R2 = (b)Compute Ra2.(Round your answer to three decimal places.) Ra2 = (c) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.The estimated regression equation did not provide a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation did not provide a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.The estimated regression equation provided a good fit as a…The following estimated regression equation based on 10 observations was presented. ŷ = 29.1260 + 0.5306x1 + 0.4680x2 The values of SST and SSR are 6,728.125 and 6,215.375, respectively. (a) Find SSE. SSE = (b) Compute R2. (Round your answer to three decimal places.) R2 = (c) Compute Ra2. (Round your answer to three decimal places.) Ra2 = (d) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.The estimated regression equation did not provide a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation provided a good fit as a large proportion of the variability in y has been explained by the estimated regression equation.
- The following table displays the mathematics test scores for a random sample of college students, along with their final SY16C grades. a. Fit the regression line y = a+bx to the data and interpret the results. b. Use the regression equation to determine the SY16C grade for a college student who scored60 on their achievement test. What would their SY16C grade be?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 exercise involving data in this and subsequent sections were designed to be solved using Excel. The following estimated regression equation is based on 30 observations. ^y = 17.2 + 3.6x1 – 2.2x2 + 7.8x3 – 2.9x4 The values of SST and SSR are 1,805 and 1,762 , respectively. Compute R2 (to 3 decimals).