3. Use least-squares regression to fit a straight line to the given data below:11 12 15 17 19.8 7 10 12 12246y56Also compute for the standard error of the estimate and the correlation coefficient.

The formula for the least squares linear regression is y=mx+b. Here, m=n∑xy-∑x∑yn∑x2-∑x2 and…

Answered: 3. Use least-squares regression to fit…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A company wishes to estimate a regression line for the relationship between sales and advertising. а. To arrive at its decision regarding the best model to use, the company has calculated the following three correlation coefficients. i. ii. The sales in any month depend on that month's advertising with r = 0.28 The sales in any month depend on 50% of the previous month's advertising and 50% of that month's advertising with r= 0.68 The sales in any month depend on the previous month's advertising with r = 0.92 iii. Interpret each of the above correlation coefficients and state which of the suggested models you would choose as the basis for predicting sales. Justify your answer.
Q3: From the following data: 2 5 y 5 4 6 3 1) Draw scatter plot. 2) Determine the regression line y = a + b x. 3) Predict the value of y for the value of x = 4.6. 4) Calculate the correlation coefficient. 4 8 3 5
Consider the following data values for variables x and y: Ť 8 10 5 2 3 1 X 5 4 3 6 9 8 10 The regression coefficients were calculated as bo = 13.223 and b₁ = -1.257. Select the correct statement. Select one: O a. If x = 2, the estimated value of y from the regression line is -25.189. b. The least--squares regression line is y = 13.223-1.257x. c. An x-value of 11 resulted in an estimated y value of -1.861 d. The least--squares regression line is y = 1.257-13.223x. e. The relationship between x and y appears to be linear and positive.
Calculate the co-efficient of correlation and obtain the least square regression lines for the following data : 3 x: . 1 2 4 5 6 7 8 9 у: 8 10 12 11 13 14 16 15 Also obtain an estimate of y which should correspond on the average to x = 6.2.
The following data represent the commute time (in minutes) x and a score on a well-being survey y. The equation of the least-squares regression line is y = - 0.0423x + 69.1961 and the standard error of the estimate is 0.5262. Complete parts (a) through (e) below. 15 25 35 45 60 82 115 D 69.0 68.3 66.8 66.2 66.5 64.2 y 67.4 (a) Predict the mean well-being index composite score of all individuals whose commute time is 30 minutes. y = (Round to two decimal places as needed.) (b) Construct a 90% confidence interval for the mean well-being index composite score of all individuals whose commute time is 30 minutes. Lower Bound (Round to two decimal places as needed.) Upper Bound |(Round to two decimal places as needed.) (c) Predict the well-being index composite score of Jane, whose commute time is 30 minutes. y =(Round to two decimal places as needed.)
- 16. Find the least squares regression line for the points (0, 8), (4, 5), (5, 3), (8,-1), and (10,-2). Round numerical values in your answer to two decimal places. a. y=-1.07x+2.63 b. y=-1.27x+8.36 c. y=-1.07x+8.36 d.y=-1.07x+10.54 c. y=-1.27x+2.63
According to the nutrition research, recommendation on the consumption of fiber for children and teenagers is the following (y is the amount of fiber per day (in grams), x is the age): y 20 22 26 29 31 33 37 40 41 2 4 6 8 10 12 14 16 18 ४ = (a) Test for the significance of regression using the analysis of variance with a useful linear relationship between these two variables? We (b) Estimate ². Round your answer to three decimal places (e.g. 98.765). (c) Estimate the standard error of the slope and intercept in this model. Round your answers to three decimal places (e.g. 98.765). (B₁) se (Bo) se B = = conclude that the model specifies a useful linear relationship at a = 0.05. Mo 0.05. Can you conclude that the model specifies a
The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, ŷ = bo + b₁x. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.05 level of significance. Critical Values of the Pearson Correlation Coefficient Average Temperature (°F) Average Temperatures and Snow Accumulations 42 31 24 45 38 18 33 21 25 9 12 27 7 15 22 30 13 20 37 Snow Accumulation (in.) 8
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b. Consider the following data, Study Hours (Y) Sleeping Hours (X) 2 4 8. 10 13 7 10 8 7 7 i) Calculate and analyze the fitted regression line between the number of study hours and the number of sleeping hours of different intakes of CSE students. ii) Find the coefficient of determination and interpret your data. iii) Predict study hour when he/she sleeps 11 hours.
Given below are five observations collected in a regression study on two variables x (independent variable) and y (dependent variable). X Y 10 7 20 5 30 4 40 2 50 1 a. Develop the least squares estimated regression equation. b. At the 5% level of significance, perform a t test and determine whether or not the slope is significantly different from zero. d. Compute the coefficient of determination. e. Compute the coefficient of correlation.

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3. Use least-squares regression to fit a straight line to the given data below: 11 12 15 17 19. O 2 4 6 9 y 6 7 6 8 7 10 12 12 Also compute for the standard error of the estimate and the correlation coefficient.