a) Find the least square regression line for the following set of data {(-1 , 0),(0 , 2),(1 , 4),(2 , 5)} b) Plot the given points and the regression line in the same rectangular system of axes.
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a) Find the least square regression line for the following set of data
{(-1 , 0),(0 , 2),(1 , 4),(2 , 5)}
b) Plot the given points and the regression line in the same rectangular system of axes.
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- Does Table 1 represent a linear function? If so, finda linear equation that models the data.Over a period of ten years, the number of times a certain individual has visited New York each year has been recorded. Records have also been kept of the number of incidents of major jewelry thefts in the city for each year in this period. The numbers are as follows: 17 15 22 14 9 18 10 5 Visits(xi) Thefts (yi) 6 12 5 Slope = 6 Intercept = 8 a) Determine the equation of the regression line. b) Estimate the percentage of thefts that are explained by this person's number of visits to the city each year. c) Is there a significant linear correlation between the number of visits and the number of thefts? Enter your answers below. Use 6 decimal places. 3 Use 6 decimal places. STRICTLY FOLLOW THE DECIMAL PLACES REQUIRED IN THIS PROBLEM. 7 Percentage of thefts that are explained by this person's number of visits to the city each year = Is there a significant linear correlation between the number of visits and the number of thefts (Yes or No)? - 21 5 13 51. Consider the following set of points: {(-2 , -1) , (1 , 1) , (3 , 2)}a) Find the least square regression line for the given data points.b) Plot the given points and the regression line in the same rectangular system of axes
- Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(1, 4), (3, 6), (5, 11), (7, 15), (11, 23)}The applet displays a scatterplot with the following points: (7,10),(27,35),(24,25),(8,12),(10,19),(15,22). Identify the slope of the regression line, intercept of the regression line, and correlation coefficient. Report your answers accurate to within two decimal places.The table below shows the amounts of crude oil (in thousands of barrels per day) produced by a country and the amounts of crude oil (in thousands of barrels per day) imported by a country, for the last seven years. Construct and interpret a 90% prediction interval for the amount of crude oil imported by the this country when the amount of crude oil produced by the country is 5,603 thousand barrels per day. The equation of the regression line is Oil produced,x Oil imported, y -1117x+ 15,844.101. 5,158 5,093 5,008 10,026 5,822 5.724 5,651 5,449 9,328 9,131 9,667 10,088 10,145 10,199 Construct and interpret a 90% prediction interval for the amount of crude oil imported when the amount of crude oil produced by the country is 5,603 thousand barrels per day Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) O A. There is a 90% chance that the predicted amount of oil imported is between thousand barreis, when there are…
- A researcher collected statistics on the sales amount of a product in 120 different markets and the advertising budgets used in TV, radio and newspaper media channels for each of these markets. The sales amount are expressed in 1000 units, and the budgets are expressed in 1000$. The researcher wants to create a simple linear regression model by choosing one among the TV, radio and newspaper advertising budgets to explain the amount of sales. Accordingly, answer the following question by using the data in the "Regression Data Set" document in the appendix. 1) a) In your opinion, which variable should this researcher choose as an independent variable to the simple regression model? Explain your decision by providing its statistical basis.A researcher collected statistics on the sales amount of a product in 120 different markets and the advertising budgets used in TV, radio and newspaper media channels for each of these markets. The sales amount are expressed in 1000 units, and the budgets are expressed in 1000$. The researcher wants to create a simple linear regression model by choosing one among the TV, radio and newspaper advertising budgets to explain the amount of sales. Accordingly, answer the following question by using the data in the "Regression Data Set" document in the appendix.1) b) In your opinion, which variable should this researcher choose as an independent variable to the simple regression model? Establish the simple linear regression model using the argument of your choice and write the equation for the model. Interpret b0 and b1.1) c) Test whether there is a statistically significant and linear relationship between the independent variable and the dependent variable by establishing the relevant…We have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.
- when a regression is used as a method of predicting dependent variables from one or more independent variables. How are the independent variables different from each other yet related to the dependent variable?4) Use computer software to find the multiple regression equation. Can the equation be used for prediction? A wildlife analyst gathered the data in the table to develop an equation to predict the weights of bears. He used WEIGHT as the dependent variable and CHEST, LENGTH, 4)_ and SEX as the independent variables. For SEX, he used male-1 and female=2. WEIGHT CHEST LENGTH SEX 344 45.0 67.5 1 416 54.0 72.0 1 220 41.0 70.0 360 49.0 68.5 332 44.0 73.0 1 140 32.0 63.0 436 48.0 72.0 1 132 33.0 61.0 356 48.0 64.0 150 35.0 59.0 1 202 40.0 63.0 365 50.0 70.5 1 A) WEIGHT = 196 + 2.35CHEST + 3.40LENGTH + 25SEX; Yes, because the R2 is high. B) WEIGHT =-320+10.6CHEST + 7.3LENGTH-10.7SEX; Yes, because the P-value is high. C) WEIGHT =-442.6 + 12.1CHEST + 3.6LENGTH- 23.8SEX; Yes, because the adjusted R² is high. D) WEIGHT = 442.6+ 12.1CHEST + 4.2LENGTH– 21SEX; Yes, because the P-value is low. %3D |D %3DThe equation of the line containing the points (−2,−4) and (2,5) is y=2.25x+0.5. Compute the sum of the squared residuals of the given data set for this line. The sum of the squared residuals for the line containing the points (−2,−4) and (2,5) is