5. (3) Indicate if each of the following statements about the simple linear regression modeltrue or false and explain why(a). The simple regression line estimated by the method of Least Squared passes through thesample mean of dependent and independent variable.(b). The slope estimator of the Least Squares regression line is free of measure.(c). The sample covariance between the residuals from the least square regression and theexplanatory variable is zero.(d). If the values of x more widely spread out, the estimate of the slope coefficient is less concise.(e). Adjusted R-squared will always increase when an additional independent variable is added intothe regression.

The simple linear regression model shows the relationship b/w 1 independent variable and 1 dependent…

Answered: 5. ( 3) Indicate if each of the…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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?
Show that an interaction term of a dummy variable and a regressor changes the slope of a regression line..
answer true or false and explanation please.
The number of pounds of steam used per month at a plant is thought to be related to the average monthly ambient temperature (in ◦F). The past year’s usages and temperatures follow.
3
Interpret the least squares regression line of this data set. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The correct least squares regression line for the data set is: y = 8.116x + 273.273 Use it to complete the following sentence: The least squares regression line predicts an additional annual rainfall if the average temperature of coastal waters increases by one degree millimetres of Celsius.
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?
Let’s assume a particular sample of Math classes contains several student GPAs from a minimum of 3.3 and a maximum of 4.0. The researcher would like to use a regression line to make estimations for future students who take this class and eventually graduate. Another student in a History class whose GPA is 3.1 would also like to use this regression line. (a) Can this regression line be used for the History student? Explain.
The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. ..... (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. y=x+O Data for licensed drivers by age and gender. (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Find the least-squares regression line for females. x + Number of Number of Number of Male Fatal Number of Female Fatal (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Licensed Drivers Crashes Licensed Drivers Crashes (b) Interpret the slope of the least-squares regression line for each gender, if appropriate. How might an insurance…
Suppose there is 1 dependent variable (dissolved oxygen, Y) and 3 independent variables (water temp X1, depth X2, and hardness of water X3). Below is the result of the multiple linear regression.Which of the three independent variable(s) is (are) significant predictor(s) of dissolved oxygen? water temperature only since its p-value is less than 0.05 level of significance intercept only since it has the greatest t statistic depth and hardness since their p-values are greater than 0.05 level of significance water temperature and intercept since their p-values are less than 0.05 level of significance
4. A runner was tested on a treadmill. During the test, his speed x (in km/h) and his heart rate y were measured. The results are shown in the table. y 122 132 145 161 178 190 x 8 10 12 14 16 18 (a) Test for the significance of regression using the analysis of variance with a = 0.05. Find the P-value for this test. Can you conclude that the model specifies a useful linear relationship between these two variables? (b) Estimate ². (c) Estimate the standard error of the slope and intercept in this model. (d) Test the hypothesis that the increase in the speed of 1 km/h results in the runner's heart rate average increase of 7 points at a = 0.05. Suppose that the alternative hypothesis is that the average increase of the runner's heart rate in this situation does not equal 7 points.

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