EBK BUSINESS STATISTICS
7th Edition
ISBN: 8220102743984
Author: STEPHAN
Publisher: PEARSON
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Students have asked these similar questions
2. The instructor of a mathematics class collected data to see whether there is a correlation
between the number of absences (X) and the student's score on the final exam (Y). The
number of absences and score on the final exam were recorded. The following regression
equation was obtained: Final score = 92.5317 – 3.7611 (Absences)
a) (5 points) What would be the predicted final exam score for a student that had 10
absences?
b) (5 points) The student from part (a) actually scored a 60 on the final exam. What is the
residual for this student? Show all work.
A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a
regression analysis was performed, and a portion of the computer output is as follows:
ŷ = 4.5+ 14.4x
Coefficients
(Intercept)
x
Estimate
4.5
Ho: B₁ = 0
H₁: B₁ > 0
Ho: B₁ = 0
Ha: B₁ <0
14.4
Ho: B₁ = 0
Ha:
B₁ #0
Std. Error Test statistic
2.9
4.7
1.55
3.06
P-value
Specify the null and the alternative hypotheses that you would use in order to test whether a linear
relationship exists between x and y.
0.07
0
Which of the following is NOT a plot of residuals typically used in multiple regression analysis with two independent variables (X1 and X2)?
Select one:
a.
Residuals versus X2.
b.
Residuals versus correlation coefficients.
c.
Residuals versus time.
d.
Residuals versus X1.
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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?arrow_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forward
- The distance between the Y value in the data and the predicted Y value from the regression equation is known as the residual. What is the value for the sum of the squared residuals? a. SSresidual = r2(SSX) b. SSresidual = r2(SSY) c. SSresidual = (1 – r2)(SSX) d. SSresidual = (1 – r2)(SSY)arrow_forwardA study wants to access the relationship between volume and weight of batch of logs of wood (100 logs). It turns out that the scale used to measure the weight is not working appropriately, and every time a log of wood is measured, the next mesaurement will be 1 lb more than it should be (eg. for the 10th log, the scale will read 10 lb more than their actual weight). Identify the assumption of regression that would be violated in this situation. If the experiemnters figured out this problem at the 100th measurement, can anything be done such that the data might still be used?arrow_forwardConsider the model Ci= B0+B1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The number of degrees of freedom for this regression is A. 2950 OB. 2948 OC. 2952 OD. 2arrow_forward
- A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.3 14.9x Coefficients (Intercept) X Estimate St 4.3 Ho: B₁ = 0 Ha: B₁ > 0 B1 O Ho: B₁ Ha: B₁ <0 = 0 14.9 B1 O Ho: B₁ = 0 0 Ha: B1 Std. Error Test statistic P-value 2.9 5.1 1.48 Specify the null and the alternative hypotheses that you would use in order to test whether a negative linear relationship exists between x and y. 2.92 0.08 0.01arrow_forward4. A simple linear regression is fit to a dataset. Unfortunately, the corresponding ANOVA table is not complete because some quantities in the table are missing due to unknown digital errors. Calculate the missing values, denoted by "?", in the ANOVA table based on the other available values. Is this regression model significant (α = 0.05)? Source Regression Residual Total df ? ? 21 SS ? ? ? MS = SS/df ? 1.13 F-Ratio 430.65 p-value ?arrow_forwardSuppose the estimaited OLS regression is: Happiness = a + b*dailychocolates Now use chocolate consumprion per week instead of days. What is the relationship between the old and new units? How would this affect b (i.e. what is bnew in terms of b)?arrow_forward
- This table reports the regression coefficients when the returns of the size-institutionalownership portfolio (columns 1 and 2) returns are regressed on three variables: a constant(column 3), the stock market returns (column 4), and the change of the value weighted discountof the closed end fund industry (column 6). Columns 5 and 7 report the corresponding t-statistics of the coefficient estimates. Note that a t-statistic with an absolute value above 1.96means the coefficient estimate is significantly different from 0 at the 1% level. Column 8reports the R square of the regressions. Column 9 reports the mean institutional ownership ofeach portfolio. The last column reports the F-statistics for a multivariate test of the null hypothesis that the coefficient on ΔVWD in the Low (L) ownership portfolio is equal to theHigh (H) ownership portfolio. Two-tailed p-values are in parentheses. 1. What is the main finding of this Table? 2. What is the explanation for…arrow_forwardplease see attached .arrow_forwardSuppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ?X is the age of the crab in months and ?ˆY^ is the predicted value of ?Y, the size of the male crab in cm. ?ˆ=9.1367+0.4817��Y^=9.1367+0.4817X What is the value of ?ˆY^ when a male crab is 22.1725 months old? Provide your answer with precision to two decimal places.arrow_forward
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