Consider the following data on y = number of songs stored on an MP3 player and x = number of months the user has owned the MP3 player for a sample of 15 owners of MP3 players. x y 22 485 34 748 2 81 28 581 5 117 32 728 23 445 10 128 4 61 26 476 1 35 8 121 13 266 9 126 5 141

Consider the following data on y = number of songs stored on an MP3 player and x = number of months the user has owned the MP3 player for a sample of 15 owners of MP3 players. x y 22 485 34 748 2 81 28 581 5 117 32 728 23 445 10 128 4 61 26 476 1 35 8 121 13 266 9 126 5 141

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

See similar textbooks

Related questions

Q: The following data were collected during a study of consumer buying patterns: Observation y 1 15 74…

A: (1) Use EXCEL to construct the scatter plot. EXCEL procedure: Go to EXCEL Go to Insert menu…

Q: Determine the equation of the regression line for the following data, and compute the residuals.…

A: Computation: From the table, the summary of quantities are,

Q: The following data has mid term marks and end term marks of 9 students. Maximum marks for both…

A: The given dataset is: x y 67 55 59 42 73 80 63 83 89 76 78 67 64 63 28 33 89 58

Q: 6. Consider the following set of data points: 2 4 14 20 23 25 Y 2 6 14 20 12 19 Construct a scatter…

A: Scatter plot is the graphical representation of the relationship between two variables of a…

Q: Listed below are paired data consisting of movie budget amounts and the amounts that the movies…

A: Given data, X Y X*Y X*X 45 108 4860 2025 19 11 209 361 116 97 11252 13456 73 68 4964 5329…

Q: The data on the right are birth rate and income ratio for a sample of 12 developing countries.…

Q: The following table gives the aptitude test scores and productivity indices of 10 workers selected…

Q: For a sample of 8 employees, a personnel director has collected the following data on ownership of…

A: As per our guidelines we can solve first three subpart and rest can be reposted. Solution-: X=Years…

Q: The following data on price ($) and the overall score for 6 stereo headphones that were tested by…

A: For the given data find all the required blanks

Q: Use the given data to find the equation of the regression line. Examine the scatterplot and identify…

A: Given that : X Y X \cdot YX⋅Y X^2X2 Y^2Y2 10 7.11 71.1 100 50.5521 8 6.44 51.52 64…

Q: Based on the data shown below, calculate the regression line. y 1 44.75 2 43.56 40.27 4 34.98 33.19…

Q: A manufacturer of optical lenses has the following data on the cost per unit of a certain custom…

Q: You are given the following data: 1. Find the least square regression line. Y = ax+b 2. Estimate the…

A: Given data: X 0 1 2 3 4 5 6 7 8 9 10 Y 12 14 18 21 26 29 31 34 36 38 40 1) To find the least…

Q: What is the equation of the regression line?

A: Answer:

Q: 1. Consider the following data of the number of hours 12 students spent online during the weekend…

A: (a) Use EXCEL to obtain the value correlation coefficient r: EXCEL procedure: Go to EXCEL Go…

Q: What is the slope of the regression line when predicting Y from X? X Y 11 13 9 9…

Q: For the following data, if a correlation coefficient of r = 0.9679 is calculated, how much of the…

A: We know that the percentage of variation is the dependent variable that can be explained by an…

Q: The following data on price ($) and the overall score for 6 stereo headphones that were tested by…

Q: Assume the following table lists campaign spending, in thousands of dollars, by candidates for…

A: In this case, Spending is the independent variable (x) and Percentage of the popular vote (y), is…

Q: Listed below are paired data consisting of movie budget amounts and the amounts that the movies…

Q: Consider the following data on x- weight (pounds) and y price ($) for 10 road-racing bikes. Brand…

A: Level of significance = α = 0.05 Weight Price($) 17.8 2100 16.1 6250 14.9 8370 15.9 6200…

Q: The following data represent a set of 10 experimental runs in which two independent variables X1 and…

A: Solution Given That the fallowing data data set represents a set of 10 experimental runs in which…

Q: Use the following data to perform a regression analysis. What is the null hypothesis? What is the…

A: Given that X Y X \cdot YX⋅Y X^2X2 Y^2Y2 1 132 132 1 17424 2 131 262 4 17161 3 134…

Q: 2. The following data represent the Statistics grade and intelligence test administered by the…

A: For the given data we have to calculate correlation coefficient, regression equation, scatterplot…

Q: Based on the data shown below, calculate the regression line. 2 10.02 3 11.58 4 9.84 5 9.3 9.46 7…

Q: Consider the following data set z represents the month, y represents the number of dialysis patients…

A: Given: X represents the month Y represents the number of dialysis patients

Q: A paper gave the following data on n = 11 female black bears. Age (years) Weight (kg) Home-Range…

A: Regression

Q: You may need to use the appropriate technology to answer this question. Consider the following data…

A: Correct option: Option 5

Q: For a sample of 8 employees, a personnel director has collected the following data on ownership of…

A: Given, For a sample of 8 employees, a personnel director has collected the following data on…

Q: The following table gives information on the incomes (in thousands of dollars) and charitable…

A: Note: Since you have posted a question with multiple subparts, we will solve the first three…

Q: Consider the following data for a dependent variable y and two independent variables, a1 and x2; for…

A: According to question given that SST=15,182.9 and SSR=14,052.2 x1 x2 y 30 12 94 47 10 108…

Q: 30. The following data represents the number of days absent, x, and the final grade, y, for a sample…

A: Given : No. of absences x Final Grade y 0 89.2 1 86.4 2 83.5 3 81.1 4 78.2 5 73.9…

Q: Numbers of a particular type of sports cars sold in five different towns are given below, together…

Q: A random sample of 9 statistics students produced the following data, Midterm Exam Score, x Final…

A: Given data: Midterm Exam Score, x Final Exam Score, y 81 49 62 23 76 84 26 58 96 33…

Q: Suppose we know the following information about a set of bivariate data: Var(x)=Var(x)=6.95…

A: Given that var(x)=σx2=6.95 Cov(x,y)=σxy=-2.54 var(y)=σy2=7.45 So standard deviation of x is…

Q: The following table shows, for a sample of towns in Great Britain, the number of solicitors, x, and…

A: As per our guidelines, we are allowed to answer first three sub-parts. Thanks Given Data : X Y…

Q: An air conditioning company located in Central Florida collected data for the number of air…

A: Instruction : "hello I just need help with the first two parts " a) Given Data : X = Outside…

Q: Run a regression analysis on the following bivariate set of data with y as the response variable. y…

Q: Suppose the following table shows the data from the truck Oman company problems, Time 8.7 9.2…

A: The null and alternative hypotheses are given as follows: Variables: Here, Deliveries is dependent…

Q: The following is a regression of credit scores based on an individual's age, income, their location…

A: For statement A Since the regression is run on individual and not on city therefore the regression…

Q: An air conditioning company located in Central Florida collected data for the number of air…

A: Instruction : " hello I just need help with the 3rd and fourth part " Given Data : XX = Outside…

Q: A statistical program is recommended. A sales manager collected the following data on x years of…

A: The regression equation is ŷ = 83 + 4x, where x is the years of experience and y is the annual sales…

Q: The personnel director of a large hospital is interested in determining the relationship (if any)…

A: Solution

Q: 1) Freeze Inc. is an air conditioning company located in Lakeland, Florida. They collected data for…

A: Given information: Outside Temperatures Sales 68 4 72 5 78 8 81 10 84 14 86 15 89…

Q: What is the predicted response value? (Report answer accurate to one decimal place.) y =…

A: Given : X Y 43.8 54.1 41.3 51.2 35.3 60.1 48.1 44.9 42.8 51.8 44.7 50.8 39.4…

Q: A random sample of 11 students produced the following data, where x is the hours spent per month…

Q: Consider the following data set. x 1 2 3 4 5 y 2.2 2 1.9 1.6 1.1 Find the equation of the…

A: see below the calculation

Q: The following table shows SAT scores for the past 5 years since a new experimental science program…

A: Let Year be denoted by x and Average SAT score by y. Calculate the following values. x y ( x -…

Q: Consider the following data, Study Hours (Y): 2, 4 ,6 ,8 ,10 ,13, 7 Sleeping Hours (X): 10, 9, 8,…

A: Study Hours (Y) Sleeping Hours (X) X2 Y2 XY 2 10 100 4 20 4 9 81 16 36 6 8 64 36 48 8 7 49…

Q: The following table contains the number of grams of water and the number of grams of carbohydrate…

A: a) In this case water (x) is the independent variables and Carbs (y) is the dependent variable.…

Question

Consider the following data on y = number of songs stored on an MP3 player and x = number of months the user has owned the MP3 player for a sample of 15 owners of MP3 players.

x	y
22	485
34	748
2	81
28	581
5	117
32	728
23	445
10	128
4	61
26	476
1	35
8	121
13	266
9	126
5	141

What is the equation of the estimated regression line? (Round your numerical values to four decimal places.)

y =

Is the simple linear regression model useful for describing the relationship between x and y? Test the relevant hypotheses using a significance level of 0.05. Calculate the test statistic. (Round your answer to two decimal places.)

t =

find the P-value for this test? (Round your answer to four decimal places.)

P-value=

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 95% of the residuals would lie within ______. −3.50 and +3.50 −1.75 and +1.75 −0.95 and +0.95 −0.68 and +0.68 −0.97 and +0.97
The following data shows the dexterity test scores of five assembly-line employees of Dimples Company Limited and their respective hourly productivity.Employee Score on dexterity test (?) Ali 12Kofi 14Kwesi 17Abudu 16Nana 11Units produced in an hour (?) 55636770 51You are required to(i) Write the regression equation(ii) Interpret the regression equation(iii) Calculate the Pearson’s Product Moment Correlation Coefficient.(iv) Interpret the correlation coefficient (v) Suppose the dexterity test score is 13, what would be the units produced in an hour? (vi) Clearly explain (in detail) the difference between regression analysis and correlation analysis.
4.For a sample of 12 observations, a businessman wants to regress the price (in dollar) of the laptop (Y) on the processor's speed (X). The summary results of the observations are given below. Σx = 19.8 , Σy = 24798, Σxy = 431882 Σx^2 = 33.88, Σγ^2 = 57365692 (b)Find the fitted regression line of the price of laptop on processor speed. (c) Find the predicted price of the laptop (y) for the processor speed x-1.9. (d) Compute the coefficient of determination and comment.
Consider the following computer output from a multiple regression analysis relating the price of a used car to the variables: age of car, mileage, and safety rating. Coefficients Coefficients Standard Error t� Stat P-value Intercept 42465.6942465.69 5320.545320.54 7.9817.981 0.00000.0000 Age (Year) −21096.02−21096.02 2551.522551.52 −8.268−8.268 0.00000.0000 Mileage(in Thousands) −1312.73−1312.73 103.02103.02 −12.743−12.743 0.00000.0000 Safety Rating 1533.821533.82 165.72165.72 9.2559.255 0.00000.0000 Does the sign of the coefficient for the variable safety rating make sense?
Ten observations were provided for a dependent variable y and two independent variables x1 and x2; for these data, SST = 15,177.6 and SSR = 14,056.5. (a) Compute R2. (Round your answer to three decimal places.) R2 = (b)Compute Ra2.( Round your answer to three decimal places.) Ra2 = (c)Does the estimated regression equation explain a large amount of the variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to one decimal place.) (Select Yes OR No) after adjusting for the number of independent variables in the model, we see that ______% of the variability in y has been accounted for.
Consider the following summary from from a simple linear regression involving a very small data set of n = 5 observations. Coefficients: Estimate Std. Error Intercept 9.8758 0.4882 Slope 0.5704 0.7287 Suppose all of our usual regression assumptions are met. If we wish to test the null hypothesis that there is no linear relationship between X and Y, what is the value of the appropriate t test statistic? (Give your numeric response to 3 decimal places. Give only your numeric response, and not any extra characters or symbols.)
The following is a partial computer output of a multiple regression analysis of a data set containing 20 sets of observations on the dependent variableThe regression equation isSALEPRIC = 1470 + 0.814 LANDVAL + 0.820 IMPROVAL + 13.5 AREA Predictor Coef SE Coef T P Constant 1470 5746 0.26 0.801 LANDVAL 0.8145 0.5122 1.59 0.131 IMPROVAL 0.8204 0.2112 3.88 0.0001 AREA 13.529 6.586 2.05 0.057 S = 79190.48 R-Sq = 89.7% R-Sq(adj) = 87.8% Analysis of Variance Source DF SS MS Regression 3 8779676741 2926558914 Residual Error 16 1003491259 62718204 Total 19 9783168000 For the problem above, we want to carry out the significance test about the coefficient of LANDVAL, what is the t-value for this test, and is it significant? 46.66, significant 2.05, significant 1.59, not significant 0.26, not significant
Jimmy tested a sample with of n=4 pairs of X and Y scores and found SSY = 48 and a Pearson correlation between X and Y of r = 0.4 Calculate whether the Fobserved in this regression experiment is significant at the ∞ = o.01 level
Determine the equation of the regression line for the following data, and compute the residuals. x 14 8 19 12 5 y 47 34 59 43 23 Do not round the intermediate values. (Round your answers to 3 decimal places.) y^= +( )x Do not round the intermediate values. (Round your answers to 3 decimal places.) x y Residuals 14 47 8 34 19 59 12 43 5 23
Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.73360.7336 R Square 0.53810.5381 Adjusted R Square 0.51800.5180 Standard Error 2140.27632140.2763 Observations 49 ANOVA dfdf SSSS MSMS F� Significance F� Regression 22 245,430,999.7671245,430,999.7671 122,715,499.8836122,715,499.8836 26.789226.7892 1.9E-081.9E-08 Residual 4646 210,716,007.0084210,716,007.0084 4,580,782.76114,580,782.7611 Total 4848 456,147,006.7755456,147,006.7755 Coefficients Standard Error t� Stat P-value Lower 95%95% Upper 95%95% Intercept 14276.146814276.1468 2,531.84252,531.8425 5.63865.6386 0.0000010040.000001004 9179.81229179.8122 19,372.481419,372.4814 Education (Years) 2349.95952349.9595 338.5500338.5500 6.94126.9412 0.0000000110.000000011 1668.49371668.4937 3031.42533031.4253 Experience (Years) 833.6183833.6183…