In the regression model ŷ = a + bx, a and b are the:
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A: Given equation Y^=3X+8
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- Fourteen hikers were surveyed at Algonquin Park, and asked for how many days have you been hikingand far did your travel in that time? The equation for the linear regression line is y+3x + 10.3 where x is the number of days and y is the distance travelled. Does the data include an outlier? and if so which point? Number of days hiked 1 1 2 3 3 5 5 6 7 7 9 10 11 12 Distance Traveled (km) 12 17 18 19 21 23 25 23 30 31 37 39 41 52Researchers used the simple linear regression model to study the relationship between social media screen time during a week and end-of-week quiz results. As one of the researchers, find the predicted quiz score if a student spends 18.46 hours during the next week using social media. Use the data in the table below to build the estimated regression equation and then use this equation to find the predicted quiz score: Social media weekly time, hours 14.5 3.7 30.4 34.23 2.7 16.8 13.6 4,7 20,6 4.9 Round your answer to 2 decimals. Less I Quiz results, out of 100 76.8 98.45 57.6 45.5 74.78 75.7 93.67 57.8 35.7 94.8The table shows the numbers of new-vehicle sales (in thousands) in the United States for Company A and Company B for 10 years. The equation of the regression line is y = 0.991x + 1,222.81. Complete parts (a) and (b) below. New-vehicle sales (Company A), x New-vehicle sales (Company B), y 4,149 3,923 3,566 3,400 3,266 3,076 2,868 2,485 1,952 2,066 4,912 4,871 4,827 4,721 4,672 4,474 4,684 3,822 2,956 2,754 (a) Find the coefficient of determination and interpret the result. r² = r2 = 0.821 (Round to three decimal places as needed.) How can the coefficient of determination be interpreted? The coefficient of determination is the fraction of the variation in new-vehicle sales for Company B that can be 2 explained by the variation in new-vehicle sales for Company A and is represented by The remaining fraction of the variation, 1-2, is unexplained and is due to other factors or to sampling error. s (b) Find the standard error of estimates and interpret the result. Se O (Round to three decimal…
- The following data show the brand, price (S), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ý = 22.522 + 0.335x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 78 B 150 73 95 63 70 58 E 70 38 35 26 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST = SSR = SSE = (b) Compute the coefficient of determination rt. (Round your answer to three decimal places.) 12 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. O The least squares line did not provide a good fit as a small proportion of the variability in y…Fourteen hikers were surveyed at Algonquin Park, and asked for how many days have you been hikingand far did your travel in that time? The equation for the linear regression line is y+3x + 10.3 where x is the number of days and y is the distance travelled. Estimate the number of whole days a hiker would need to travel 35KM? Number of days hiked 1 1 2 3 3 5 5 6 7 7 9 10 11 12 Distance Traveled (km) 12 17 18 19 21 23 25 23 30 31 37 39 41 52A set of data consists of the number of years that applicants for Foreign Service jobs have studied German and the grades that they received on a proficiency test. The following regression equation is obtained: y-hat = 31.6 + 10.9x, where x is the number of years of study and y is the grade on the test. Identify the predictor and response variables. a. The number of years of study is our predictor variable; the scores on the test are our dependent variable. b. Not enough information is provided to determine c. Who cares? d. The scores on the test are our predictor variable; the number of years of study is our dependent variable.
- The scatterplot below shows Olympic gold medal performances in the long jump from 1900 to 1988. The long jump is measured in meters. Use the regression line to predict the average predicted long jump distance in 1950. A. The average predicted long jump distance in 1950 is 7.94 meters. B. The average predicted long jump distance in 1950 is 362.7 meters. C. The average predicted long jump distance in 1950 is 3,054 meters. D. The average predicted long jump distance in 1950 is 6.893 meters.A biology student is investigating the claim that the temperature can be predicted by counting cricket chirps. She has found a linear regression equation T=42.2+0.21r, where T is the temperature in degrees Fahrenheit and r is the number of chirps per minute. What is the predicted temperature for 90 chirps per minute? 18.9 degrees 227.6 degrees 23.3 degrees 61.1 degreesA linear regression model has three features: x1, x2, x3. The t-stat value for each feature is -150, 110, -70, respectively. You want to build a simpler model by deleting one of the features, from your dataset. Which feature you can safely remove from the data? a. Cannot decide b. x3 c. x2 d. x1
- The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 22.391 + 0.326x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 76 B 150 71 C 95 63 D 70 56 E 70 40 F 35 24 #1) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST = SSR = SSE = #2) Compute the coefficient of determination r2.(Round your answer to three decimal places.) r2 = #2a) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) A) The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. B) The least squares line provided a good fit as a large…In multiple regression, when all independent variables are considered but the order in which they are added to the model is determined by the amount it contributes to the dependent variable, it is called: a.Two step b.Stepwise c.Simultaneous d.Backward stepd. Draw the regression line on the scatter diagram using the yp points.e. Find y for x = 50 x 20 10 30 40 60 70 y 20 20 30 50 60 80
