In a regression model involving 30 observations, the following estimated regression equation was obtained: ŷ = 17 + 4x1 − 3x2 + 8x3 + 8x4 For this model, SSR = 700 and SSE = 100. The critical F value at 95% confidence is _____. a. 2.76 b. 2.69 c. 2.53 d. 2.99
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ŷ = 17 + 4x1 − 3x2 + 8x3 + 8x4
For this model, SSR = 700 and SSE = 100.
The critical F value at 95% confidence is _____.
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- 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?In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 For this estimated regression equation, SST = 1,855 and SSR = 1,810. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) Suppose variables x1 and x4 are dropped from the model and the following estimated regression equation is obtained. ŷ = 11.1 − 3.6x2 + 8.1x3 For this model, SST = 1,855 and SSR = 1,755. (b)Compute SSE(x1, x2, x3, x4). SSE(x1, x2, x3, x4) (c)Compute SSE(x2, x3). SSE(x2, x3)= (d)Use an F test and a 0.05 level of significance to determine whether x1 and x4 contribute significantly to the model. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value =Which of the following assumptions is not necessary for unbiasedness of a slope coefficient in a multiple regression model? MLR1 MLR 4 Homoskedasticity Random sampling
- In a regression model involving 44 observations, the following estimated regression equation was obtained. For this model Model SS = 600 and Residual SS = 400. The computed F statistics for testing the overall significance of the above model isUse the following linear regression equation to answer the questions. x1 = 1.7 + 3.9x2 – 8.5x3 + 2.2x4 Suppose x2 increased by 2 units. What would be the expected change in x1? Suppose x2 increased by 4 units. What would be the expected change in x1? (e) Suppose that n = 18 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.454. Construct a 99% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit ? upper limit ? (f) Using the information of part (e) and level of significance 10%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t ? t critical ± ?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 quadratic regression equation shown below is for a sample of n=22. Determine the critical value(s).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…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 R2
- In a regression analysis involving 18 observations and four independent variables, the following information was obtained. Multiple R = .6000 R Square = .3600 Standard Error = 4.8000 Based on the above information, fill in all the blanks in the following ANOVA table. Is the model significant? ANOVA df SS MS F Regression ? ? ? ? Error ? ? ? Total ? ?A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…The accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter The predicted y-hat value for a diameter of 201 is 864. if we observed a weld that had a diameter of 235 that had a strength 1000, what would be its residual?
