2 3. 4 5 3 7 11 14 a. Develop the estimated regression equation for these data (to 1 decimal). b. Select a correct scatter diagram of the residuals against y.
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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?A set of n = 15 pairs of X and Y values has a correlation of r = +0.80 with SSY = 75, and the regression equation for predicting Y is computed. Find the standard error of estimate for the regression equation. How big would the standard error be if the sample size were n = 30.Assume that variables xx and yy have a significant correlation, and that the line of best fit has been calculated as ˆy=1.4x+3.6y^=1.4x+3.6. One observation is (9,16.3)(9,16.3).What is the predicted value of yy for the value x=9x=9? What is the residual for the value x=9x=9? What is the best interpretation for the residual? The value 16.316.3 is below the average value for yy when x=9x=9 The value 99 is above the average value for yy when y=16.3y=16.3 The value 16.316.3 is above the average value for yy when x=9x=9. The value 16.316.3 is below the average value for xx when y=16.3
- 1)Write the regression equation that represents the above equation. Y = 9.804326378 + 0.65795*X1 + 0.200358 X2 Height of an individual = 9.8043 + 0.6579*Mother's Height + 0.2004* Father's Height 2)Is this a good predictor equation? Why or why not (use appropriate statistics/hypothesis test to prove your point)?(1) Write out the regression equation (2) What is the sample size used in this investigation? (3) Determine the values of *, ** and ***, ****If other factors are held constant and the Pearson correlation value between X and Y is r = 0.80, then the regression equation will tend to produce more accurate predictions than would be obtained if the Pearson correlation value was r = 0.60. Group of answer choices True False
- If a sample of 25 pairs of data yields a correlation coefficient, r, of 0.390 and the scatterplot displays a linear trend, can you use the regression equation to make predictions, assuming your x-values are within the domain of the data set? Choose your answer from the multiple choice answers below A.) Yes, because rcrit = 0.396 and the regression coefficient, r, is less than this value. B.) Yes, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. C.) No, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. D.) No, because rcrit = 0.396 and the regression coefficient, r, is less than this value.Consider the following regression equation specied for 2-period panel data: where i = 1; 2; :::N and t = 1; 2. If you expect that β_1 is positive, but the correlation between Δx_i and Δu_i is negative, thenwhat is the bias in the OLS estimator of β_1 in the first-differenced equation?7. In a simple regression, if MSR=6400 and MSE=100, then the t statistic that we use to test the significance of the estimated slope is _____. Select one: 8 2 14 6
- 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.Jimmy tested a sample with of n=4 pairs of X and Y scores and found SSY = 48 and a Pearson correlation between X and Y of r = 0.4 Calculate whether the Fobserved in this regression experiment is significant at the ∞ = o.01 levelIn a study of possible correlation between the height in cm (X) and the weight in kg (Y) of chimpanzees, a sample of 40 animals produces a correlation coefficient of r=0.813 and a regression line with equation Y=0.34X+19.5. What is the expected weight of a chimpanzee that is 157 cm tall? Round off final answer to 2 decimal places.
