Explain why it can be dangerous to use the least-squares line to obtain predictions for x values that are substantially larger or smaller than those contained in the sample.The least-squares line is based on the x values ---Select---✓the sample. We do not know that the same linear relationship will apply for x values ---Select--- the range of values in the sample. Therefore the least-squares line should not be used for x values ---Select--- the range of values in the sample.

We have to explain:Why it can be dangerous to use the least-squares line to obtain predictions for x…

Answered: Explain why it can be dangerous to use…

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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The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year Using technology, what is the slope of the least-squares regression line and what is its interpretation? period. The results are given in the table. The slope is 1.98, which means for each additional 35 inch in height, the child's weight will increase by 1.98 Weight (x) 8. 12 18 24 30 32 37 40 30 32 33 36 38 pounds. Helght (v) 22 23 26 35 The slope is 1.98, which means for each additional inch in height, the child's weight is predicted to increase by 1.98 pounds. The slope is 0.50, which means for each additional pound in weight, the child's height will increase by 0.5 inches. The slope is 0.50, which means for each additional pound in weight, the child's height is predicted to increase by 0.5 inches.
Beachcomer Ltd is a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model. SALES = a+BAGE + yMIL + SENG Where SALES = amount that a vehicle is sold for (000's), AGE = age of vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Coef StDev t-ratio p-value Predictor Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 * 0.5042 MIL -0.7527 0.3586 -2.0991 ** ENG 4.8124 0.6196 7.7664 0.0000…
more than others. To investigate, they measured the grey matter density in two regions of the brain that are known to be associated with social perception and memory. They also recorded the number of Facebook friend of each study subject. The scatterplot below shows the relationship between these two variables along with the least squares fit. Note that grey matter density has been reported as a standardized z-score for each individual. Do not round in intermediate calculations for this problem. Round your results to 4 decimal places except where indicated below. -2 -1 1 Grey Matter Density 002 009 00s 007 001 Facebook Friends
One day in gym class students took a physical fitness test bydoing push-ups and sit-ups. The standard deviation of the number of sit-ups they were able to do was 7 and the stand-ard deviation of the number of push-ups was 2. A Statistics student used these data to create a least squares regressionline to predict the number of sit-ups a student was able to dobased on the number of push-ups the student did. Which ofthe following could NOT be the slope of that line?A) -2 B) -0.5 C) 1D) 3 E) 4
A music critic was interested in whether particular variables measured on a song change over time. Two variables the critic considered were a song’s Tempo (in bpm) and a song’s Danceability. We will use the songs written before the year 2000 from the original SpotifySample data set. The data set that you will use to complete this investigation is called SpotifyB2000 and consists of 483 songs. Write the least-squares regression line equation describing Year and Danceability usingproper notation and values. Interpret the slope of the regression line for Year and Danceability in context. Would the interpretation of the y-intercept for Year and Danceability be meaningful? Ifso, interpret it. If not, state why not in one sentence. Calculate and record the coefficient of determination value r2for Year and Danceabilityand interpret this value in context. State the hypotheses for the test of the slope. Write the p-value found in the output from (n), and use the p-value provided in the…
3. In a study of 1991 model cars, a researcher computed the least-squares regression line of price (in dollars) on horsepower. He obtained the following equation for this line. Price = -6677 + 175 × Horsepower
Beachcomer Ltd is a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model. SALES = a+BAGE + yMIL + SENG Where SALES = amount that a vehicle is sold for (000's), AGE = age of vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Coef StDev t-ratio p-value Predictor Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 * 0.5042 MIL -0.7527 0.3586 -2.0991 ** ENG 4.8124 0.6196 7.7664 0.0000…
Beachcomer Ltd is a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model. SALES = a+BAGE + yMIL + SENG Where SALES = amount that a vehicle is sold for (000's), AGE = age of vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Coef StDev t-ratio p-value Predictor Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 * 0.5042 MIL -0.7527 0.3586 -2.0991 ** ENG 4.8124 0.6196 7.7664 0.0000…
Describe in your own words what it means to perform a linear least squares analysis. Provide an example to substantiate your claims
Beachcomer Ltd is a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model. SALES = a+BAGE + yMIL + SENG Where SALES = amount that a vehicle is sold for (000's), AGE = age of vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Coef StDev t-ratio p-value Predictor Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 * 0.5042 MIL -0.7527 0.3586 -2.0991 ** ENG 4.8124 0.6196 7.7664 0.0000…
In a study of 1991 model cars, a researcher computed the least-squares regression line of price (in dollars) on horsepower. He obtained the following equation for this line. Price = – 6677 + 175× Horsepower Based on the least-squares regression line, what would we predict the cost to be of a 1991 model car with horsepower equal to 200? If the actual cost of a 1991 car with 200 horsepower is $27500, what is the residual? Is the predictionan underestimate or an overestimate? What does the slope of 175 and y intercept of (0,-6677) mean in the context of the problem? The coefficient of determination is ?2=84%. Interpret in the context of the problem. Find the correlation and interpret.
Using the guide of the textbook and your RQ, determine the equation of the least-square line for the following data: 1 6 3. Select the correct answer in the slope-intercept form. O y=-x+10.5 O y=-2x+11 O y=x O y=x+10 O x+y=11

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