Concept explainers
(a)
Construct a
(b)
Find the value of
Find the value of
Find the value of b.
Find the equation of the least-squares line.
Construct the line on the scatter diagram.
(c)
Find the sample
Find the value of the coefficient of determination
Mention percentage of the variation in y is explained by the least-squares model.
(d)
Check whether the claim that the population
(e)
Find the predicted weight at 30 years of age when a female baby weighs 20 pounds at 1 year.
(f)
Verify the values of
(g)
Find the 95% confidence interval for weight at age 30 of a female who weighed 20 pounds at 1 year of age.
(h)
Check whether the claim that the slope
(i)
Find a 80% confidence interval for
Interpret the confidence interval.
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Chapter 9 Solutions
Understandable Statistics: Concepts and Methods
- For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.arrow_forwardThe following three problems refer to the data sets displayed below: b 11.If the slope of the least squares regression line is negative, what else must be negative? a) The correlation (r)? b) The coefficient of determination (r)? c) The y-intercept (bo) d) More than one of the above must be negative. e) None of the above need be negative.arrow_forward1. The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working and to look at other factors affecting sleep: sleep = Bo + B1totwrk + Bzeduc + B3age + u, where sleep and totwrk (total work) are measured in minutes per week and educ and age are measured in years. (a) If adults trade off sleep for work, what is the sign of 31? (b) What signs do you think 32 and B3 will have? (c) Using the data in SLEEP75.csv, the estimated equation is sleep = 3638.25 – 0.148totwrk – 11.13educ + 2.20age, n = 706 R = 0.113. If someone works five more hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff? (d) Discuss the sign and magnitude of the estimated coefficient on educ. (e) Would you say totwrk, educ, and age explain much of the variation in sleep? What other factors might affect the time spent sleeping? Are these likely to be correlated with totwrk? 2.…arrow_forward
- Question 3. a) A Biologist is comparing intervals (m seconds) between the matting calls of a certain species of tree frog and the surrounding temperature (t degree Celsius). The following results were obtained: t 8 13 14 15 15 20 25 30 6.5 4.5 4 3 2 1 1. Fit the regression line in the form m = a + bt. 2. Interpret your estimates. 3. Use your regression line interval between matting calls when the surrounding temperature is 10 degrees. (6 marks) estimate the timearrow_forwardSuppose two variables are under study are temperature in degrees Fahrenheit (y) and temperature in degrees centigrade (x). The regression line for this situation is y = 9/5X +32. Assuming there is no error in observing temperature, What is the expected correlation coefficient in this given scenario. Answer:arrow_forwardA large policy debate revolves about the causes and consequences of child labour. Extensive child labour at early ages is often considered as harmful and there is substantial theoretical and empirical interest in determining the causes for child labour. Therefore, we would like to analyze the relationship between wealth (e.g. the number of cattle or other assets) and child labour, using household data collected in several villages in rural Africa. Suppose we have data on Y and X iv where Y, is the number of hours worked by child i in village v and X, is family wealth. a) Explain how this is related to the concept of Panel Data. b) Explain how you could estimate the relationship between wealth and child labour using pooled OLS, Random Effect (RE), Fixed Effect (FE) estimators. Write down the estimation equations and the conditions needed to guarantee consistency. Compare the FE and the OLS estimators: Is either of these two estimators based on weaker assumptions than the other? c)…arrow_forward
- Example 15.11) The following table shows the marks obtained in two tests by 10 students: Marks in Ist Test (X) 9. 8. 8 7 6. 10 4 7 Marks in 2nd Test (Y) 8 7 10 8 10 9. 8 6. (a) Find the least square regression line of Y on X. / (b) Test the hypothesis that marks in the two tests are linearly related.arrow_forwardA doctor collects data on all the men in his practice. Their daily potassium intake is 4500 mg/day, with a standard deviation of 1000 mg/day. They have an average systolic blood pressure of 150 mmHg, with a standard deviation of 10 mmHg. The two variables have correlation r = 3. -0.4. (a) One of the men is at the 25 percentile of potassium intake and 75 percentile of blood pressure. Relative to all other men at the 25th percentile potassium intake, this man's blood pressure is (circle one) smaller than average about average larger than average Justify your answer using a written explanation and/or a diagram.arrow_forward0. In a statistical study, it is found that variables z and y are correlated as follows. Find the least squares regression line in this model.arrow_forward
- The following is the result of the multiple linear regression analysis in STATISTICA, where the response Y = lung capacity of a person, xage = age of the person in years, xheight = height of the person in inches, = a categorical variable with 2 levels (0 = non- X smoke smoker, 1 = smoker), and xCaesarean = a categorical variable with 2 levels (0 = normal delivery, 1 = %3D %3D Caesarean-section delivery). b* Std.Err. Std.Err. t(720) p-value N=725 Intercept Age Height Smoke Caesarean of b 0.467772 0.017626 of b* -11.8001 0.1372 0.2790 -0.6407 -25.2263 7.7846 28.6552 -5.0142 0.000000 0.000000 0.000000 0.206427 0.026517 0.026340 0.754765 -0.074205 -0.033054 0.009735 0. 127774 0.092146 0.000001 0.022851 0.014799 0.014492 -0.2102 -2.2808 What is the predicted lung capacity of an 14-year old non-smoker whose height is 71 inches born by normal delivery? (final answer to 4 decimal places)arrow_forward1) The ratio of the regression mean square to the error mean square is: (a)Usually assumed to be 0.05 (b)The correlation coefficient (c)The covariance (d)The F ratio 2)The coefficient of determination, R2, ... a. Decreases as higher polynomial terms are included in the model b.Can be greater than 1.0 for transformed variables c.Measures the slope of the regression line d.None of these answers is correct 114 3. Assume you have experimental data that could be analyzed using a paired t-test or an unpaired t-test. If there are 22 degrees of freedom for the unpaired t-test, which value below describes the degrees of freedom for the paired t-test?arrow_forward7. Battery life has a strong, negative, linear relationship with temperature. If the least-squares regression line using xx = temperature explains 90% of the variation in battery life, which of the following must be the correlation, rr, between battery life and temperature? (A) -0.90 (B) 0.90 (C) -0.95 (D) 0.95 (E) Cannot be determined without the original data. Submit Answerarrow_forward
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