a) which for these data is 32.1470, 42.3520, or 10.0674c) that minimizes the error sum of squares, total sum of squares, or regression sum of squares…for which these data is 32.1470, 42.3520, or 10.0674 Bivariate data obtained for the paired variables x and y are shown below, in the table labeled "Sample data." These data are plotted in the scatter plot in Figure.1, which also displays the least-squares regression line for the data. The equation for this line is y=49.45-0.91x.In the "Calculations" table are calculations involving the observed y-values, the mean y of these values, and the values y predicted from the regressionequation.Sample datay21.531.024.326.025.724.327.726.229.6 22.2xSend data to ExcelAnswer the following.Calculations(-)²15.56301.95160.01512,879811.7375Column sum:32.1470(-1)²1.24321.78763.10823.82980.0986Column sum:10.0674(v-y)²25.60360.00362.68960.067613.9876Column sum:42.3520(a) The total variation in the sample y-values is given by the (Choose one)(Choose one) ▼.32-30+28+26+24-22-Figure 1which for these data is(b)The value is the proportion of the total variation in the sample y-values that is explained by the estimated linearrelationship between x and y. For these data, the value of ² is. (Round your answer to at least 2 decimalplaces.)S?FRED1 Answer the following.(a) The total variation in the sample y-values is given by the (Choose one)(Choose one)error sum of squarestotal sum of squaresregression sum of squares▼ which for these data is(b)The value is the proportion of the total variation in the sample y-values that is explained by the estimated linearrelationship between x and y. For these data, the value of ² is. (Round your answer to at least 2 decimalplaces.)(c)The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "bestfits" is used because the line has an equation that minimizes the (Choose one)which for thesedata is (Choose one) ▼X3

Given data: x y 21.5 31.0 24.3 26.0 25.7 24.3 27.7 26.2 29.6 22.2 The equation of…

(a) The total variation in the sample y-values is given by the (Choose one) (Choose one) ▼ error sum of squares total sum of squares regression sum of squares which for these data is (b) The value is the proportion of the total variation in the sample y-values that is explained by the estimated linear relationship between x and y. For these data, the value of ² is. (Round your answer to at least 2 decimal places.) (c) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best which for these fits" is used because the line has an equation that minimizes the (Choose one) data is (Choose one) ▼ L

(a) The total variation in the sample y-values is given by the (Choose one) (Choose one) ▼ error sum of squares total sum of squares regression sum of squares which for these data is (b) The value is the proportion of the total variation in the sample y-values that is explained by the estimated linear relationship between x and y. For these data, the value of ² is. (Round your answer to at least 2 decimal places.) (c) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best which for these fits" is used because the line has an equation that minimizes the (Choose one) data is (Choose one) ▼ L

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?
The student is constructing a confidence interval for the slope of the least-squares regression line. Are the conditions for constructing this interval met? A student is investigating the flight distance and airfare from Boston to several travel destinations. The cities were selected at random from a list of large cities. The scatterplot of airfare vs. flight distance, the residual plot of residual vs. flight distance, and the histogram of the residual values are shown. Image 1: Attached Image 2: Attached Image 3: A histogram of residuals has residual on the x-axis, and frequency of residual on the y-axis. Negative 80, 1; negative 60, 1; negative 20, 1; 0, 4; 20, 3; 40, 1; 60, 1. A. No, the observations are not independent of one another B. No, the association between distance and airfare is not linear. C. No, the distribution of residual values is not approximately Normal. D. No, the variability in the residuals is not roughly consistent throughout the residual plot. E. Yes,…
~We can conclude there is linear correlation between the number of TV ads and the number of cars sold because the sample size n is ____?____ and its corresponding critical value for the correlation coefficient is ___?____. Is the correlation positive or negative? . Find the equation of the least-squares regression line: ~The slope is: ___?___. Round to 2 decimal places.~The y-intercept is ___?_____ . Round to 2 decimal places. ~The equation of the line is: ___?_ ~Using the equation of the line we can predict that if the number of TV ads is 12 the number of cars sold will be ___?___. Round your final answer to the nearest whole number. ~The interpretation of the slope in the context of the problem is: __?_____ ~The interpretation of the y-intercept in the context of the problem is: __?_____ . If it is not appropriate to interpret the y-intercept answer "Not appropriate". ~The percentage of variation on the number of cars sold that can be explained by the number of TV ads is __?__%.
A researcher at a large company has collected data on the beginning salary and current salary of 50 randomly selected employees. The correlation between the data sets is r = 0.912. The summary statistics from the data collected are shown bellow: Beginning Salary Ending Salary Mean x¯=56,340 y¯=82,070 Standard deviation Sx = 5,470 Sy = 7,800 Use a complete sentence to describe the strength and direction of the linear relationship between beginning salary and current salary. Find the equation of the least-squares regression line. (Round to two decimal places)
A magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, decor, service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.
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)
Using the least-squares regression line, y=-25.5+1.5x, what is the residual for the data point at (28,19)?
1. Plot the data points on a scatter diagram. 2. Determine the equation of the regression line and find Pearson product-moment correlation coefficient. 3. Determine the point estimate of y at x = 5.5
Calculate the least square regression line Y= B0+B1 x with the formula method, justifying your choice for the dependent and independent variables. Round the parameter estimates to 2.d.p B. Calculate and interpret the value of the sample the correlation coefficient r. Carry out a t-test for the null hypothesis that the true value of the correlation coefficient is equal to 0. Report the value of the correlation coefficient and test statistic round to 2.dp C. What daily expenditure per capita on food would be predicted for a household with a daily income per capita of 30 pounds
Suppose we conduct a study on the time spent studying for an exam and exam scores. We survey students in introductory statistics and find the explanatory variable (time, in hours) ranges from 0 to 16 and exam scores (in points, out of 100 maximum) range from 5 to 100. The correlation between time spent studying and exam scores is 0.80. We fit a simple linear regression model to these data and get the following least squares line: score = 4 + 6*(time). You pick a random student from the course and observe that the number of hours she studied for the exam is 1 standard deviation above the mean time spent studying. How many standard deviations above or below the mean exam score would you expect her to score?
Data was collected on 54 observations on a response of interest, y, and four potential predictor variables x1, x2, x3, and x4. The output from regression analyses of the data is attached to the end of the page. d) Is the variable from your best simple linear regression model (from part a) included in the model with the lowest overall MSE (part b)? Briefly explain why it could happen that the best single variable is not in the best overall model. e) Following the best subsets regression results, the sums of squares for regression and error (also called residual) are displayed for several models. Using the regression sums of squares information for the full model containing all four x variables, calculate i) the R2 value for the full model, ii) the F statistic for the test of the H0: b1 = b2 = b3 = b4 = 0, and iii) the standard deviation of the residuals for the full model. f) Using the regression sums of squares information, test the null hypothesis H0:b2 = b4 = 0 for the full model.…
The owner of Showtime Movie Theaters, Inc., would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follows: Weekly Revenue (£1000s) Television advertising (£1000s) Newspaper advertising (£1000s) 96 5 1.5 90 2 2 95 4 1.5 92 2.5 2.5 95 3 3.3 94 3.5 2.3 94 2.5 4.2 94 3 2.5 a) Calculate the correlation coefficient among the variables and explain the result. b) Plot two simple linear regression equations- i) television advertising as independent variable and weekly revenue as dependent variable ii) newspaper advertising as the independent variable and weekly revenue as dependent variable. You would be using Excel Data Analysis Pack – Regression to get the relationship; c) Create scatter diagrams for each linear relationship and display the linear regression equation and R square value on chart.