Concept explainers
Mental health of a community. An article in the Community Mental Health Journal (August 2000) used multiple
- a. Write the equation of E(y) for the complete model.
- b. Give the null hypothesis for testing whether the 7 Diagnostic variables contribute information for the prediction of y.
- c. Give the equation of the reduced model appropriate for the test, part b.
- d. The test, part b, resulted in a test statistic of F = 59.3 and p- value < .0001. Interpret this result in the words of the problem.
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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_forwardLife insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below Examine both the scatterplot and the correlation matrix provided above. Comment on the apparent relationship between the customer’s age at death and their father’s age at death in the plot. Explain how the information in the correlation matrix supports your conclusionarrow_forwardWhat is the purpose of multiple linear regression?  a. To assess whether there is a significant difference between independent groups  b. To predict scores of an independent variable from scores of a single dependent variable  c. To predict scores of a single dependent variable from scores on multiple independent variables  d. To predict scores of an independent variable from scores on multiple dependent variablesarrow_forward
- What is the significance of R and R2 and of a regression model?arrow_forwardWhat is the difference between an interaction term and a main effect in multiple linear regression?arrow_forwardIn a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats' diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:ŷ = 36 + .8x1 − 1.7x2Also provided are SSR = 60 and SST = 180.The test statistic for testing the significance of the model is _____.  a. 5.00   b. .50   c. .25   d. .33arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt