We wish to determine the relationship between the years of education and the income of the economically active population in a metropolitan area. In a random sample of 10 people we have the following data Ex=115: x² = 1583; y = 129295; ² 2012627525 xy = 1741560 a) Obtain the linear regression line y = a + bx b) If a person has an income of 10,000 pesos, how many years of education do they have?
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- Can brand, battery life, and internal storage capacity affect a smartphone's price? Use MegaStat and α = .05 to perform a regression analysis for the Smartphones01BS dataset and answer the following questions. When you copy and paste output from MegaStat to answer a question, remember to choose to "Keep Formatting" to paste the text.Stoaches are fictional creatures that nest in truffula forests. A researcher wants to know whether there is a relationship between a stoach’s wingspan (?W, the predictor) and its nest height (?H, the response). A sample of 88 stoaches is observed, and for each, the wing-span (in cm) and the nest height (in m) are recorded. The observed data meet the assumptions for a linear regression, so the researcher fits the regression model and obtains a regression equation ℎ̂=−0.813+0.177?,h^=−0.813+0.177w, with standard error for the coefficient of ?w equal to 0.448. Determine the ?p-value from a test for a statistically significant linear dependence of nest height on wing-span. (Give your answer to 4 decimal places.A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.5+ 14.4x Coefficients (Intercept) x Estimate 4.5 Ho: B₁ = 0 H₁: B₁ > 0 Ho: B₁ = 0 Ha: B₁ <0 14.4 Ho: B₁ = 0 Ha: B₁ #0 Std. Error Test statistic 2.9 4.7 1.55 3.06 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a linear relationship exists between x and y. 0.07 0
- A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. A linear regression was performed on these data, and the result is the linear regression equation Yi=−0.840+1.4108Xi. Determine the coefficient of determination,r2,and interpret its meaning. Determine the standard error of the estimate. How useful do you think this regression model is for predicting opening weekend box office gross? Can you think of other variables that might explain the variation in opening weekend box office gross?What is C,D and E? And how do i calculate it??Stoaches are fictional creatures that nest in truffula forests. A researcher wants to know whether there is a relationship between a stoach’s wingspan (?W, the predictor) and its nest height (?H, the response). A sample of 85 stoaches is observed, and for each, the wing-span (in cm) and the nest height (in m) are recorded. The observed data meet the assumptions for a linear regression, so the researcher fits the regression model and obtains a regression equation ℎ̂=−4.273+0.834?,h^=−4.273+0.834w, with standard error for the coefficient of ?w equal to 0.242. Determine the ?p-value from a test for a statistically significant linear dependence of nest height on wing-span. (Give your answer to 4 decimal places.
- please use this situation: A small theater company has a linear regression model to estimate y = the concession stand sales in dollars, based on knowing x = the number of people in attendance. The regression equation is: = 6.72x + 11.50 and the correlation coefficient was r = 0.781. The data set saw the number of people in attendance ranging from a minimum of 18 people to a maximum of 170 people. 1) How reliable would it be to make a prediction for the concession sales amount if there were 500 people in attendance? Explain.A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. A linear regression was performed on these data, and the result is the linear regression equation Yi=−1.254+1.3968Xi. Complete parts (a) through (d). a. Determine the coefficient of determination,r2,and interpret its meaning. b. Determine the standard error of the estimate. c. How useful do you think this regression model is for predicting opening weekend box office gross? d. Can you think of other variables that might explain the variation in opening weekend box office gross?The table below gives the number of weeks of gestation and the birth weight (in pounds) for a sample of five randomly selected babies. Using this data, consider the equation of the regression line, y = bo + b1x, for predicting the birth weight of a baby based on the number of weeks of gestation. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Weeks of Gestation 33 34 36 38 41 Weight (in pounds) 6 6.1 6.8 7.3 7.9 Table Copy Data Step 4 of 6: Find the estimated value of y when x = 36. Round your answer to three decimal places.
- A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled " The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes and depth D is in meters. The report then says, " The regression equation for this bird is: DD = 2.33 + 0.001 D. (a) What is the slope of the regression line?. ANSWER ? minutes per meter. (b) According to the regression line, how long does a typical dive to a depth of 100 meters last? ANSWER ? minutes.A researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: FR=a+B0IL+YEXP+8FDI Where FR = yearly foreign reserves ($000°s), OIL = annual oil prices, EXP = yearly total exports ($000's) and FDI = annual foreign direct investment ($000`s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 ** s = 2.45 R-sq = 96.3% R-sq (adj) = 95.3% Analysis of Variance Source DF MS F Regression 1991.31 663.77 ?? Error 12 77.4 6.45 Total 15 a) What is dependent and independent variables? b) Fully write out the regression equation3. Wine Participant magazine has collected average price per bottle for the prestigious Chateau Le Thundebird bordeaux for different vintages (years). The data appears in the table below. year of bottling price a) draw the scatter diagram showing how wine price varies by vintage year b) use the most appropriate regression equation to determine the relationship between year of bottling (age) and price. c) what is the explanatory power (RSQ) of that equation d) determine the predicted price of a bottle of this wine for the 2017 vintage. 2009 36 2010 40 2011 51 2012 60 2013 68 2014 72 2015 70 2016 65 2018 51 2019 44 2020 39
