The least-squares regression output reports the p-value for a two-sided hypothesis test. True False
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- What is meant when a statistician talks about getting a "best fit" least squares regression line (hint: what is the mathematical relationship behind this?)4) _____ Classical hypothesis testing can give different decisions than the P-value approach even with the same level of significance, hypotheses and data? 5) _____ A well-designed experiment may give evidence of causation. 6) _____ A least-squares regression line minimizes the error of the estimates provided by the regression line over the data.(a) Calculate and write out the least-squares regression equation. (b) Calculate a 90% confidence interval for the slope ?1 of the regression. (c) Test the hypothesis that the altitude of origin affects the dark respiration rate. Write down the pair of hypotheses, specify the test statistic value or the P-value and state your conclusion of the test. Use ?=0.05 (d) For a batch of bugs collected at an altitude of 720 meters, what is the plausible range of the dark respiration rate? Provide an appropriate 95% interval (confidence interval or prediction interval). (e) What is the sample correlation coefficient?
- The null hypothesis being tested in the least-squares regression output for B is B1 = B1,0=1. True FalseThe file JTRAIN2 contains data on a job training experiment for a group of men. Men could enter the program starting in January 1976 through about mid-1977. The program ended in December 1977. The idea is to test whether participation in the job training program had an effect on unemployment prob- abilities and earnings in 1978. |(i) The variable train is the job training indicator. How many men in the sample participated in the job training program? What was the highest number of months a man actually participated in the program? |(ii) Run a linear regression of train on several demographic and pretraining variables: unem74, unem75, age, educ, black, hisp, and married. Are these variables jointly significant at the 5% level?4) In a univariate linear regression, explain intuitively, graphically and mathematically, how the variance of the estimated slope depends on a) the number of observations; b) the mean squared deviation of the independent variable; c) What else does it depend on? Can you explain how?
- An article on the cost of housing in California that appeared in the San Luis Obispo Tribunet included the following statement: "In Northern California, people from the San Francisco Bay area pushed into the Central Valley, benefiting from home prices that dropped on average $4000 for every mile traveled east of the Bay area." If this statement is correct, what is the slope of the least-squares regression line, ý = a + bx, where y = house price (in dollars) and x = distance east of the Bay (in miles)? Your answer cannot be understood or graded. More InformationAn engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.With multiple regression, the null hypothesis for the entire model now uses the p test. True False
- Suppose that you perform a hypothesis test for the slope of the population regression line with the null hypothesis H0: β1 = 0 and the alternative hypothesis Ha: β1 ≠ 0. If you reject the null hypothesis, what can you say about the utility of the regression equation for making predictions?Espan Interpreting technology: The following display from the TI-84 Plus calculator presents the least-squares regression line for predicting the price of a certain stock (y) from the prime interest rate in percent (x). LinReg y=a+bx a = 2.39562641 do b=0.37929688 2=0.4130321711 r=0.64267579 Part: 0 /3 Part 1 of 3 Write the equation of the least-squares regression line. Use the full accuracy shown in the calculator output (do not round your answers). Regression line equation: y = Part 2 of 3 What is the correlation between the interest rate and the yield of the stock? The correlation coefficient is Part: 2 /3 Part 3 of 3 Predict the price when the prime interest rate is 6%. Round the answer to at least four decimal places. When the prime interest rate is 6%, the price is predicted to beSelect all statements that are true of the least-squares regression line. ) It assumes a linear relationship between the explanatory and the response variable. R-squared is the portion of sample variance in the explanatory variable that can be explained by variation in the response variable. ) It can be used to predict the mean response of the explanatory variable. | R-squared is the portion of sample variance in the y variable that can be explained by variation in the x variable.
