Mathematical Statistics with Applications
7th Edition
ISBN: 9781111798789
Author: Dennis O. Wackerly
Publisher: Cengage Learning
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Chapter 12.2, Problem 8E
The standard error of the estimator
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If I add the additional condition which is the labor is female using the following:
#People who is femalefemale = x*0.46
Will it become dependent variable and how will I do linear regression model by adding this condition?
Find the equation for the least squares regression line of the data described below.
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.
Round your answers to the nearest thousandth.
y = L
Submit
State true or false
When a correlation coefficient for a linear regression model is close to -1 , the regression line is poor fit for the data.
Chapter 12 Solutions
Mathematical Statistics with Applications
Ch. 12.2 - Suppose that you wish to compare the means for two...Ch. 12.2 - Refer to Exercise 12.1. Suppose that you allocate...Ch. 12.2 - Suppose, as in Exercise 12.1, that two populations...Ch. 12.2 - Refer to Exercise 12.3. How many observations are...Ch. 12.2 - Suppose that we wish to study the effect of the...Ch. 12.2 - Refer to Exercise 12.5. Consider two methods for...Ch. 12.2 - Refer to Exercise 12.5. Why might it be advisable...Ch. 12.2 - The standard error of the estimator 1 in a simple...Ch. 12.3 - Consider the data analyzed in Examples 12.2 and...Ch. 12.3 - Two computers often are compared by running a...
Ch. 12.3 - When Y1i, for i = 1, 2,, n, and Y2i, for i = 1,...Ch. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - A plant manager, in deciding whether to purchase a...Ch. 12.3 - Muck is the rich, highly organic type of soil that...Ch. 12.3 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Complete the assignment of treatments for the...Ch. 12 - Prob. 28SECh. 12 - Prob. 29SECh. 12 - Prob. 30SECh. 12 - Prob. 31SECh. 12 - Prob. 32SECh. 12 - Prob. 33SECh. 12 - Prob. 34SECh. 12 - The earths temperature affects seed germination,...Ch. 12 - An experiment was conducted to compare mean...Ch. 12 - Prob. 37SE
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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_forwardTable 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?arrow_forwardTable 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forward
- The coefficients in a distributed lag regression of Y on X and its lags can be interpreted as the dynamic causal effects when the time path of X is determined randomly and independently of other factors that influence Y. Explain How?arrow_forwardSuppose you are estimating a wage regression, where salary is the dependent variable and age, years of education and a dummy variable for male are your independent variables. You are interested in measuring how salary differs between those who have at least a college education with those who have less than a college education. If a person is considered as having a college education when she has more than 12 years of education, how can you measure the difference in salary between college and non-college educated individuals? Select one: a. Multiply coefficient for years of education in original regression by 12 O b. Re-estimate model replacing years of education with a dummy variable for college c. Re-estimate model replacing years of education with a dummy variable for college and one for no college O d. Re-estimate model interacting years of education with a dummy variable for college e. Calculate the difference in predicted salary between an individual with 14 years of education and…arrow_forwardTwo variable are found to have a strong negative linear correlation. Pick the regression equation that best fits this scenario. Oŷ = 0.32x 30 Oy = 0.82x - 30 Oy y = -0.32x + 30 -0.82x + 30arrow_forward
- Suppose a random sample of 100 20-year-old men is selected from a population, and that these men’s height and weight are recorded. A regression of weight on height yields "Weight" = -79.24 + 4.16 X Height, R2 = 0.72, SER = 12.6, (3.42) (.42) where weight is measured in pounds and height is measured in inches. A man has a late growth spurt and grows 2 inches over the course of a year. Construct a 95% confidence interval for the person’s weight gain.arrow_forwardA negative correlation between variables X and Y will always result in a positive slope in the linear regression model. Cannot tell from the given information. False Truearrow_forwardWhat are the assumptions of multiple linear regressions only?arrow_forward
- Suppose the equation for a regression line is y =4x + 6. If x = 5, what is the predicted corresponding value for y?arrow_forwardAn oil exploration company wants to develop a statistical model to predict the cost of drilling a new well. One of the many variables thought to be an important predictor of the cost is the number of feet in depth that the must be drilled to create the well. Consequently, the company decided to fit the simple linear regression model, where y = cost of drilling the new well (in $thousands) and x = number of feet drilled to create the well. Using data collected for a sample of n=83 wells, the following results were obtained: = 10.5 + 16.20x Give a practical interpretation of the estimate of the slope of the least squares line. An oil exploration company wants to develop a statistical model to predict the cost of drilling a new well. One of the many variables thought to be an important predictor of the cost is the number of feet in depth that the must be drilled to create the well. Consequently, the company decided to fit the simple linear regression model, where y =…arrow_forwardRun a simple linear regression in SPSS to know if previous experience (‘prevexp’: Previous Experience-months) significantly predicts current salary(‘salary’: Current Salary) in the work force . Use α =.05 Does Previous Experience significantly predict Current Salary? Report Beta(β), and the p-value (p).arrow_forward
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