Explain which characteristic of the STA leads to a consideration of a logistic model as opposed to a linear regression mode.
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Explain which characteristic of the STA leads to a consideration of a logistic model as opposed to a linear regression
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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?when a regression is used as a method of predicting dependent variables from one or more independent variables. How are the independent variables different from each other yet related to the dependent variable?Define the Linear Regression Model. Also explain Terminology for the Linear Regression Model with a Single Regressor?
- Explain what a residual is and how this relates to the best-fit regression model.Assume that you want to predict Company Performance based on the linear effects of Trust and Commitment that exist among a company’s employees c) If you want to test whether there is a linear effect of Commitment and a curvilinear effect of Trust on Company Performance—such that Company Performance increases up to a certain level of Trust, after which Company Performance diminishes with increasing Trust levels—how would your regression equation look like? Further, explain your answer in your own words. Provide at least two sentences of explanation, in addition to giving the regression equation.What are the assumptions of multiple linear regressions only?
- An observational study was conducted where subjects were randomly sampled and then had their resting heart rate recorded, as well as their smoking status (0 for non-smoker and 1 for smoker) and how much they exercise on average each day (in hours). A linear regression model is fit where we have response variable of resting heart rate and explanatory variables of smoking status (0 for non-smoker and 1 for smoker) and exercise amount per day in hours, along with an interaction between smoking status and exercise amount. The output is below: Coefficients: Estimate Std. Error t value Pr(>t) (Intercept) 84.8172 1.9553 43.377 <2e-16 *** Smoke -2.2645 5.0665 -0.447 0.6551 Exercise -7.3684 0.8075 -9.125 <2e-16 *** Smoke: Exercise 1.9562 2.5510 0.767 0.4442 Signif. codes: O **** 0.001 (*** 0.01 *' 0.05 .' 0.1 ' 1 Residual standard error: 8.396 on 228 degrees of freedom Adjusted R-squared: Multiple R-squared: 0.2971, F-statistic: 32.13 on 3 and 228 DF, p-value: < 2.2e-16 0.2879 The model that…Let's consider a situation where a company wants to understand the relationship between its advertising expenditure and its sales revenue. This is a typical scenario where simple linear regression can be applied. The company hypothesizes that as advertising expenditure increases, sales revenue also increases. To test this hypothesis, the company can collect data on advertising expenditure and sales revenue and perform a simple linear regression analysis. Match the explanatory and response variables with the appropriate information from this description.Hormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on x = percent of women using HRT and y = breast cancer incidence (cases per 100,000 women) for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence. t HRT Use Breast Cancer Incidence 46.30 40.60 39.50 36.60 30.00 103.30 105.00 100.00 93.80 83.50 (a) What is the equation of the estimated regression line? (Round your numerical values to four decimal places.) ŷ = (b) What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to four decimal places.) cases per 100,000 women (c) What breast cancer incidence (in cases per 100,000 women) would be…
- Hormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on x = percent of women using HRT and y = breast cancer incidence (cases per 100,000 women) for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence. HRT Use Breast Cancer Incidence 46.30 103.30 40.60 105.00 39.50 100.00 36.60 93.80 30.00 83.50 n USE SALT (a) What is the equation of the estimated regression line? (Round your numerical values to four decimal places.) ý = (b) What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to four decimal places.) cases per 100,000 women (c) What breast cancer incidence (in cases per 100,000 women)…What is regression models?Hormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on x = percent of women using HRT and y = breast cancer incidence (cases per 100,000 women) for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence. HRT Use Breast Cancer Incidence 46.30 103.30 40.60 105.00 39.50 100.00 36.60 93.80 30.00 83.50 n USE SALT (a) What is the equation of the estimated regression line? (Round your numerical values to four decimal places.) ý = 45.5727 + (1.3354 )x (b) What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to four decimal places.) 1.3354 cases per 100,000 women (c) What breast cancer incidence…
