X Y 1 2.5 4.4 1 2 13.6 4 20.7 4 25.6 36.2 5 Using the formulas for linear regression, find the constants for the regression model given by y aoa1. Then use the linear model to determine the expected value of Y when x 3
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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?Y7 a multiple regression model includes two explanatory variablesy= 10+0.6x+0.8zbased on the above relationship what is the expected change in y if x increase by 10 and y decrease by 5?
- Using the linear regression line from the sample, y = a + b x + e, if b = 0 then R 2 = 0. True/FalseA fitted linear regression model is (y=10+2x ). If x = 0 and the corresponding observed value of y = 9, the residual at this observation is:Assume that there is a positive linear correlation between the variable R (return rate in percent of financial investment) and the variable t (age in years of the investment) given by the regression equation R = 2.5t + 5.3. 1- Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? 2- If the investment continues to grow at a constant rate, what is the expected return rate when the investment is 7 years old? 3- If the investment continues to grow at a constant rate, how old is the investment when the return rate is 32.8%?
- You have obtained a sub-sample of 1744 individuals from the Current Population Survey (CPS) and are interested in the relationship between weekly earnings and age. The regression, using heteroskedasticity-robust standard errors, yielded the following result: = 239.16 + 3.75× Age, R2 = 0.15, SER = 287.21., where Earn and Age are measured in dollars and years respectively. Interpret the intercept? Interpret the slope coefficient b) Is the effect of age on earnings large? The average age in this sample is 37.5 years. What is annual income in the sample? (e) Interpret the measures of fit.The Pearson correlation between X1 and Y is r = 0.40. When a second variable, X2, is added to the regression equation, we obtain R2 = 0.64. How much variance for the Y scores is predicted by using both X1 and X2 as predictor variables? 0.40 or 40% 0.64 or 64% 0.48 or 48% 0.16 or 16%Consider a simple linear regression model Y=α+βX+ε. We have collected 15 samples, from which we calculated the summary statistics ∑xi=66, ∑x2i=6568, ∑yi=459, ∑y2i=27933, ∑xiyi=11311. Suppose one of the data is supposed to be (x1=10, y1=30), but is incorrectly recorded as (x1=7, y1=34). All other observations are correctly recorded. What is the OLS estimators αˆ= ? and βˆ= ? based on the correct data.
- A surgery intern has conducted a study of the sleeping habits of her colleagues and has developed a following regression equation: y-hat = 6 + 0.1X, where X is the number of hours working on one shift, and Y is the number of hours sleeping at night after that shift. Yvette worked 10 hours and slept 8 hours. What is Yvette’s residual? 0.1 1 6 7A set of n = 4 pairs of X and Y values has a Pearson correlation of r = 0.60 and SSY = 200. The standard error of estimate for the regression equation is _______. a. 8 points b. 10 points c. 6 points d. 4 points(a) The standard error Se of the linear regression model is given in the printout as "S." What is the value of Se?