Exercise 7.30 presents regression output from a model for predicting the heart weight (in g) of cats from their body weight (in kg). The coecients are estimated using a dataset of 144 domestic cats. The model output is also provided below. Estimate Std. Error t value Pr(>|t|) (Intercept) body wt -0.357 0.692 -0.515 0.607 4.034 0.250 16.119 0.000 s = 1.452 R? = 64.66% Radi 64.41% a) What are the hypotheses for evaluating whether body weight is positively associated with heart weight in cats? Ho: B1 = 0; HA: ß1 # 0 Ho: B1 = 0; HA: B1 > 0 Ho: Bo = 0; HA: Bo > 0 Ho: Bo = 0; HA: Bo # 0 b) State the conclusion of the hypothesis test from part (a) in context of the data. O The data provide convincing evidence that body weight is positively associated with heart weight in cats. OThe data does not provide convincing evidence that body weight is positively associated with heart weight in cats. ) The data provide convincing evidence that body weight is negatively associated with heart weight in cats. O The data does not provide convincing evidence that body weight is negatively associated with heart weight in cats. c) Calculate a 95% confidence interval for the slope of body weight. Round to 2 decimal places.

Exercise 7.30 presents regression output from a model for predicting the heart weight (in g) of cats from their body weight (in kg). The coecients are estimated using a dataset of 144 domestic cats. The model output is also provided below. Estimate Std. Error t value Pr(>|t|) (Intercept) body wt -0.357 0.692 -0.515 0.607 4.034 0.250 16.119 0.000 s = 1.452 R? = 64.66% Radi 64.41% a) What are the hypotheses for evaluating whether body weight is positively associated with heart weight in cats? Ho: B1 = 0; HA: ß1 # 0 Ho: B1 = 0; HA: B1 > 0 Ho: Bo = 0; HA: Bo > 0 Ho: Bo = 0; HA: Bo # 0 b) State the conclusion of the hypothesis test from part (a) in context of the data. O The data provide convincing evidence that body weight is positively associated with heart weight in cats. OThe data does not provide convincing evidence that body weight is positively associated with heart weight in cats. ) The data provide convincing evidence that body weight is negatively associated with heart weight in cats. O The data does not provide convincing evidence that body weight is negatively associated with heart weight in cats. c) Calculate a 95% confidence interval for the slope of body weight. Round to 2 decimal places.

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...

See similar textbooks

Similar questions

What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
What is regression analysis? Describe the process of performing regression analysis on a graphing utility.
Table 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?
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?
Can the average rate of change of a function be constant?
Table 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?
Shown below is a portion of a computer output for a linear regression analysis relating an individual's income (y in thousands of dollars) to age (x1 in years), level of education (x2 ranging from 1 to 5), and the individual's gender (x3 where 0 = female and 1 = male). Coefficient Standard Error t-statistic p-value Intercept 15.934 1.389 11.47 0.000 x1 0.625 0.094 6.65 0.000 x2 0.921 0.190 4.85 0.000 x3 –0.510 0.920 –0.55 0.590 Source of Variation Sum of squares Degrees of freedom Mean square F-statistic p-value Regression 84 3 28 4 0.027 Error 112 16 7 Total 196 19 a. Is there a significant relationship between an individual's income and the set of variables, age, level of education, and gender (based on a significance level α =05 )? Explain why using one of the p-values in the output tables. b.Which of the three predictor variables are…
A highway employee performed a regression analysis of the relationship between the number of construction work-zone fatalities and the number of unemployed people in a state. The regression equation is Fatalities = 12.7 + 0.000114 (Unemp). Some additional output is: Predictor Coef SE Coef T P Constant 12.726 8.115 1.57 0.134 Unemp 0.00011386 0.00002896 3.93 0.001 Analysis of Variance Source DF SS MS F P Regression 1 10,354 10,354 15.46 0.001 Residual Error 18 12,054 670 Total 19 22,408 a. How many states were in the sample? b. Determine the standard error of estimate. (Round your answer to 2 decimal places.) c. Determine the coefficient of determination. (Round your answer to 2 decimal places.) d. Determine the correlation coefficient. (Round your answer to 2 decimal places.)
In a regression context, under what situation is the predicted value for Y equal to the mean of Y?
The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 43 inches. Is the result close to the actual weight of 237 pounds? Use a significance level of 0.05. Chest_size_(inches) Weight_ (pounds)50 27954 33944 21954 29240 20136 116 Is the result close to the actual weight of 237 pounds? A. This result is close to the actual weight of the bear. B. This result is very close to the actual weight of the bear. C. This result is not very close to the actual weight of the bear. D. This result is exactly the same as the actual weight of the bear.
The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value? Chirps in 1 min 888 910 1071 844 1039 1241 Temperature (°F) 78.1 79.6 82.9 76.4 79.4 87.3 What is the regression equation? y=_______+_______x