From the SPSS output table for a bivariate regression, identify the number that will indicate the "slope" of the linear function. Model 1 (Constant) Income a. Dependent Variable: Price O.873 O.564 7.598 O.074 Coefficients Unstandardized Coefficients B 8286.786 564 Std. Error 1852.256 074 Standardized Coefficients Beta 873 t 4.474 7.598 Sig. 000 .000
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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?Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semi-fragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P14_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semi-fragile cargo.Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2
- Given a generic data set (x,y) with a linear regression. How do you determine if the y(dependent) will be less/greater than a certain value at a decided value of x?The owner of Original Italian Pizza restaurant chain wants to understand which variable most strongly influences the sales of his specialty deep-dish pizza. He has gathered data on the monthly sales of deep-dish pizzas at his restaurants and observations on other potentially relevant variables for each of several outlets in central Indiana. These data are provided in the file P10_04.xlsx. Estimate a simple linear regression equation between the quantity sold (Y) and each of the following candidates for the best explanatory variable: average price of deep-dish pizzas (X1), monthly advertising expenditures (X2), and disposable income per household in the areas surrounding the outlets (X3). Round your answers for intercept coefficients to the nearest whole number and slope coefficients to two decimal places, if necessary. If your answer is negative number, enter "minus" sign.The systolic blood pressure dataset (in the third sheet of the spreadsheet linked above) contains the systolic blood pressure and age of 30 randomly selected patients in a medical facility. What is the equation for the least square regression line where the independent or predictor variable is age and the dependent or response variable is systolic blood pressure? Y=__________ X + ______________ Patient 7 is 67 years old and has a systolic blood pressure of 170 mm Hg. What is the residual? __________ mm Hg Is the actual value above, below, or on the line? What is the interpretation of the residual? (difference in actual &predicated bp, difference in age, the amount of systolic changes)
- A researcher was investigating variables that might be associated with the academic performance of high school students. The data included the average Math SAS score of all high school seniors in the city that took the exam (labeled as the variable SAT-M), the average number of dollars per pupil spent on education by the city (labeled as the variable $Per Pupil), and the percentage of high school seniors in the city that took the exam (labeled as the variable %Taking). The researcher ran the following multiple linear regression model as SAT-M=Beta0 + Beta1($Per Pupil) + Beta2(%Taking). This model was fit to the data using the method of least-squares, results shown inside of table within photo. If we want to test using ANOVA F-test with hypotheses Ho: Beta1=Beta2=0 versus H1: at least one of the Beta is not 0, what would the value of our F-statistic mean?In a simple linear regression, show that the OLS regression line always passes through the mean (average) of both x and y.The linregress() method in scipy module is used to fit a simple linear regression model using “Reaction” (reaction time) as the response variable and “Drinks” as the predictor variable. The output is shown below. What is the correct regression equation based on this output? Is this model statistically significant at 5% level of significance (alpha = 0.05)? Select one. Python script outputs for the linregress method. Slope equals 6.0000, intercept = 3.9999, rvalue = 0.9728, pvalue = 0.0011, stderror = 0.7141. Note: Python output shows many decimal places. All values Question 2 options: Reaction = 6.0000 + 3.9999 Drinks, model is not statistically significant Reaction = 6.0000 + 3.9999 Drinks, model is statistically significant Reaction = 3.9999 + 6.0000 Drinks, model is not statistically significant Reaction = 3.9999 + 6.0000 Drinks, model is statistically significant
- Given a generic data set (x,y) with a linear regression. How do you determine if the y(dependent) will be less than a certain value?You spilled water on your calculations from (a) and can't remember what your estimated regression parameters are. But you do have two possible estimated errors for each of your initial four observations:When is the standard error of the estimate (in linear regression) large? When the X values are very close to the Y values. When the residuals are large on average. When the average distance between actual Y scores and predicted Y scores is small. When the coefficient of determination is small.