?0=?(??|??=0) b. ?0 is the estimated average change in the value of ?? when we change the value of ?? c. ?0 is the predicted value of ?? when ??=0 d. ?0=?(??|??=0)
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Consider the linear regression model ??=?0+?1??+?? and assume that ?(??|??)=4 for each ?=1,...,?. Which one of the following is true about the interpretation of ?0?
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- The population (in millions) and the violent crime rate (per 1000) were recorded for 10 metropolitan areas. The data are shown in the following table. Do these data provide evidence to reject the null hypothesis that ? = 0 in favor of ? ≠ 0 at ? = .05? (Give your answers correct to three decimal places.) Population 10.4 2 3.4 6 6.2 1.2 2.7 3.1 0.8 5 Crime Rate 12.6 8.9 7.5 8.9 7.8 9.3 8 7.4 8.6 9.3 (a) Calculate r. _______(ii) Calculate the critical region._____ (smaller value) ______(larger value)(b) State the appropriate conclusion. Reject the null hypothesis, there is not significant evidence that ? ≠ 0.Reject the null hypothesis, there is significant evidence that ? ≠ 0. Fail to reject the null hypothesis, there is not significant evidence that ? ≠ 0.Fail to reject the null hypothesis, there is significant evidence that ? ≠ 0.A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below. Vacation Days 5 15 13 3 9 0 3 7 7 14 4 Sick Days 5 5 1 5 4 9 9 6 5 3 9 Use the model to predict the number of sick days taken for an employee who took 3 vacation days this year.Sick Days = ? (Please round your answer to the nearest whole number.) Interpret the slope of the regression line in the context of the question: As x goes up, y goes down. The slope has no practical meaning since a negative number cannot occur with vacation days and sick days. For every additional vacation day taken, employees tend to take on average 0.40 fewer sick days. Interpret the y-intercept in the context of the question: The y-intercept has no practical meaning for this study. If an employee takes no vacation days, then that employee will take 8 sick days. The average number of sick days is…Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of |r| large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use ? = 0.01. (Round your answer for r to four decimal places.) x 1004 975 992 935 970 928y 40 100 65 145 70 151 r = ______critical r = ______
- Suppose that a regression line is found to be ý = 0.5470x +7.7000 What is the predicted value for a = 7? O a. 11.53 O b. 54-45 C. 53-35 O d. -3.87Which one of the following statements is true? The correlation coefficient is not affected by outliers. O In the context of correlation and regression, as long as the correlation is strong, it's okay to infer that the explanatory variable causes the response variable. O The "P" in P-value stands for "practical." O The slope in a regression equation tells us what we predict y to be if x is equal to 0 O It is not necessary to know the population size in order to compute the standard deviation of the sampling distribution.Q9 The explanatory variable in linear correlation/regression model is recorded on which of thesemeasurement scales: A. categorical B. ordinal C. quantitative D. none of the above
- Which one of the following statements is true? When predicting one quantitative variable based on another, the variable you are trying to predict should always go on the x-axis of the scatterplot. The intercept in a regression equation can never negative. The correlation coefficient has no units. A very strong relationship between variables can result in a value of r that is larger than 1. A correlation coefficient can only range in value from 0 to 1.Which of the following is a true attribute of a regression line? A. A regression line is a tool for making predictions about future observed values for center variables B. A regression line reduces a linear relationship to its bare essential. C. A regression line allows us to analyze a relationship without being distracted by small details. D. all of the above27. What percentage of the variability is accounted for by the regression model?A. 1% B. 2% C. 98% D. 99%28. Is there a linear relationship between the dependent variable and the independent variables?A. Cannot be knownB. MaybeC. NoD. Yes29. What will be the value of y if x = 0?A. -12.87 B. -0.08 C. 0.70 D. 0.99
- longley is a built-in R data.frame which is sometimes used in economics to study regression. We are interested in some descriptive statistics related to the Employed column of the longley data.frame. We can access this data directly by using the assignment x <- longley$Employed (In R, use ? Longley for info on this data) The values of x if assigned as above are: [1] 60.323, 61.122, 60.171, 61.187, 63.221, 63.639, 64.989, 63.761 [9] 66.019, 67.857, 68.169, 66.513, 68.655, 69.564, 69.331, 70.551 You should get these values from the R assignment above rather than manually entering the data. b. Calculate the 3rd quartile of x using the R summary function c. Calculate the sample range & median of x h. What proportion of the x values are less than 1 sample standard deviation from the sample mean? k. How many of the elements of x are smaller than the sample mean of x?Q6 Given a data set where the response variable is normalized ( centered ) and it is know that the correlation between the individual predictor variable & response variable is, r 0.9. And, it is found that S,-10 and X=100. (i) Find B= a. Write the formula for B= (ii) Find B= (iii) (iv) Find the value the predictor, which yields the response variable to be 1 X Q7 There are several assumptions which are needed to be verified prior to using a univariate regression model and/or doing any traditional model analysis ( e.g. need to verify these assumptions prior to doing the actual regression or F/T tests etc ). Write down the two most essential mathematical assumptions needed by explaining them in a brief written statement (i) 1" = (ii) 2* = answer both questions pleseIf all the points in a scatter plot fall precisely on the regression line then the correlation is____ choose one perfect or negative or positive