In multiple regression testing of where a p-value of 0.08, would give an indication that the null hypothesis should _____ a. None of these b. not be rejected c. be rejected d. all independent variables have a slope of zero
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4Olympic 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?Test the null hypothesis that the slope is zero versus the two-sided alternative in the following setting using the alpha=0.05 signifiance level. n=20, yhat=28.5+1.4x, and SEb1=0.65
- In simple linear regression, most often we perform a two-tail test of the population slope 1 to determine whether there is sufficient evidence to infer that a linear relationship exists. The null hypothesis is stated as:A scientist is interested in whether there is a linear relationship between the amount of mercury in a lake and the surface area of the lake. The scientist collected data on 22 lakes of a similar type selected at random and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim. H0:β=0 Ha:β≠0 The test yielded a t-value of 2.086 with a corresponding p-value of 0.05. Which of the following is the correct interpretation of the p-value? A. If there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic as extreme as 2.086 or more extreme is 0.05 B. If there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 is 0.05. C. If there is not a linear relationship between the amount of mercury in a lake and the surface area of the lake, the…A scientist claims that there is a linear relationship between a lake’s flow rate and its runoff factor. The scientist collected data and used the data to test the claim that there is a linear relationship at a significance level of α=0.05α=0.05. The scientist tested the following hypotheses. H0: β1=0 Ha: β1≠0 The scientist found a p-value of 0.02 for the test. Which of the following is a correct conclusion about the scientist’s claim? A. The null hypothesis is rejected since 0.02<0.05. There is sufficient statistical evidence to suggest that there is a linear relationship between a lake’s flow rate and runoff factor. B. The null hypothesis is not rejected since 0.02<0.05. There is sufficient evidence to suggest that there is a linear relationship between a lake’s flow rate and runoff factor. C. The null hypothesis is rejected since 0.02<0.05. There is not sufficient evidence to suggest that there is a linear relationship between a lake’s flow rate and runoff factor. D.…
- A major credit card company is interested in whether there is a linear relationship between its internal rating of a customer’s credit risk and that of an independent rating agency. The company collected a random sample of 200 customers and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim. H0:β1=0Ha:β1≠0 The test yielded a t-value of 3.34 with a corresponding p-value of 0.001. Which of the following is the correct interpretation of the p-value? If the alternative hypothesis is true, the probability of observing a test statistic at least as extreme as 3.34 is 0.001. If the alternative hypothesis is true, the probability of observing a test statistic at least as extreme as 3.34 is 0.001. A If the alternative hypothesis is true, the probability of observing a test statistic of 3.34 or greater is 0.001. If the alternative hypothesis is true, the probability of observing a test statistic of 3.34 or greater…A researcher recorded the number of e-mails received in a month and the number of online purchases made during that month for 50 people with an online presence. The resulting data were used to conduct a hypothesis test to investigate whether the slope of the population regression line relating number of e-mails received to number of online purchases is positive. What are the correct hypotheses for the test? H0:β1=0Ha:β1≠0H0:β1=0Ha:β1≠0 A H0:β1=0Ha:β1>0H0:β1=0Ha:β1>0 B H0:β1=0Ha:β1<0H0:β1=0Ha:β1<0 C H0:β1>0Ha:β1=0H0:β1>0Ha:β1=0 D H0:b1=0Ha:b1≠0 EA manufacturer of car batteries claims that the mean lifetime of their battery is 67 months. Thinking that this claim is inflated, graduate students buy a random sample of 72 car batteries from this manufacturer. How should they proceed? a) Perform a hypothesis test of H0:μ=67 versus Ha:μ>67 b) Perform a hypothesis test of H0:μ=67 versus Ha:μ<67 c) Use Simple linear regression
- Q6. The outcome variable in a linear regression is best measured on which of the following scales? a. CategoricalB. ContinuousC. Ordinal D. None of the aboveWhich of the following is not an example of systematic error in an observational study? A cross-sectional study recruits participants that are willing to sign up outside of a major university and meet the inclusion and exclusion criteria to take part in the survey relating unsafe sex habits to STIs. A researcher is interested in the relationship between coffee drinking and lung cancer, and after careful multivariate linear regression modeling determines that a significant percentage of the relationship is due to another variable, cigarette smoking. An observational study recruits participants for a study looking at Alzheimer’s disease due to exposure to industrial hazards by asking participants to recall their exposure over the past 10 years. data-entry specialist responsible for adding in fasting glucose levels to a database accidentally skipped an observation during the input phase of data cleaning.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.