The accompanying data file contains 40 observations on the response variable y along with the predictor variables x and d. Consider two linear regression models where Model 1 uses the variables x and d and Model 2 extends the model by including the interaction variable xd. Use the holdout method to compare the predictability of the models using the first 30 observations for training and the remaining 10 observations for validation. y x d 70 11 1 102 19 1 76 12 1 83 14 1 61 17 0 62 13 0 67 20 0 98 16 1 84 11 1 101 15 1 51 16 0 108 16 1 32 13 0 71 15 1 101 17 1 90 15 1 112 19 1 88 13 1 110 18 1 95 17 1 44 14 0 51 19 0 112 17 1 113 17 1 52 13 0 61 10 1 100 16 1 78 14 1 90 16 1 57 16 0 59 15 0 53 15 0 119 19 1 109 18 1 68 11 0 104 19 1 45 18 0 67 17 0 65 15 0 74 14 1 1. Use the training set to estimate Models 1 and 2. Note: Negative values should be indicated by a minus sign. Round your answers to 2 decimal places. 2. Calculate the RMSE of the two models in the validation set. Note: Do not round intermediate calculations and round final answers to 2 decimal places.

The accompanying data file contains 40 observations on the response variable y along with the predictor variables x and d. Consider two linear regression models where Model 1 uses the variables x and d and Model 2 extends the model by including the interaction variable xd. Use the holdout method to compare the predictability of the models using the first 30 observations for training and the remaining 10 observations for validation. y x d 70 11 1 102 19 1 76 12 1 83 14 1 61 17 0 62 13 0 67 20 0 98 16 1 84 11 1 101 15 1 51 16 0 108 16 1 32 13 0 71 15 1 101 17 1 90 15 1 112 19 1 88 13 1 110 18 1 95 17 1 44 14 0 51 19 0 112 17 1 113 17 1 52 13 0 61 10 1 100 16 1 78 14 1 90 16 1 57 16 0 59 15 0 53 15 0 119 19 1 109 18 1 68 11 0 104 19 1 45 18 0 67 17 0 65 15 0 74 14 1 1. Use the training set to estimate Models 1 and 2. Note: Negative values should be indicated by a minus sign. Round your answers to 2 decimal places. 2. Calculate the RMSE of the two models in the validation set. Note: Do not round intermediate calculations and round final answers to 2 decimal places.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2
Given are data for two variables, x and y. xi 6 11 15 18 20 yi 5 8 13 19 30 (a) Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.) ŷ = (b) Compute the residuals. (Round your answers to two decimal places.) xi yi Residuals 6 5 11 8 15 13 18 19 20 30 Compute the standardized residuals. (Round your answers to two decimal places.) xi yi Standardized Residuals 6 5 11 8 15 13 18 19 20 30
The monthly premium quoted by an insurance company for a critical illness policy was collected from a sample of 6 adult male smokers at different age. The data for the sample are shown: Age 28 25 50 39 47 31 Premium ($) 75 40 175 125 250 105 Using Age to predict premium, the Linear Regression equation is given by: ŷ =6.556X−112 and r2=0.813y^=6.556X−112 and r2=0.813 a. Identify the independent and Dependent variables. Dependent: Age Premium Independent: Age Premium b. Determine the slope. Slope = Slope = Round to 3 decimal places c. Determine |r||r| . |r|=|r|= Round to 3 decimal places d. Interpret rr : and e. Determine critical r value at 5% significance level and determine if there is a significant linear correlation exists. |r| critical=|r| critical= Round to 3 decimal places Linear Correlation:Linear Correlation: Significant Not Significant f. Predict the monthly premium for a 40 years old adult male smoker.…
Consider a simple linear regression model with predictor variable x and response variable y, where the regression line is represented by the equation y = β0 + β1x. If β0 = -5 and β1 = 3, what is the predicted value of y for a given x = 4?
The owner of Original Italian Pizza restaurant chain wants to understand which variable most strongly influences the sales of his specialty deep-dish pizza. He has gathered data on the monthly sales of deep-dish pizzas at his restaurants and observations on other potentially relevant variables for each of several outlets in central Indiana. These data are provided in the file P10_04.xlsx. Estimate a simple linear regression equation between the quantity sold (Y) and each of the following candidates for the best explanatory variable: average price of deep-dish pizzas (X1), monthly advertising expenditures (X2), and disposable income per household in the areas surrounding the outlets (X3). Round your answers for intercept coefficients to the nearest whole number and slope coefficients to two decimal places, if necessary. If your answer is negative number, enter "minus" sign.
In a multiple linear regression model with 3 predictor variables, what is the t-statistic for the hypothesis test of the null hypothesis that the coefficient of the second predictor variable is equal to 0, if the estimated coefficient is 0.5, the standard error of the estimate is 0.1, and the degrees of freedom is 15?
In a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats' diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:ŷ = 36 + .8x1 − 1.7x2Also provided are SSR = 60 and SST = 180.The test statistic for testing the significance of the model is _____. a. 5.00 b. .50 c. .25 d. .33
Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.04, standard error for the coefficient of z is 0.01, and the sample size is 20. Can we conclude that advertising expenditure is a statistically significant variable?
In a typical multiple linear regression model where x1 and x2 are non-random regressors, the expected value of the response variable y given x1 and x2 is denoted by E(y | 2,, X2). Build a multiple linear regression model for E (y | *,, *2) such that the value of E(y | x1, X2) may change as the value of x2 changes but the change in the value of E(y | X1, X2) may differ in the value of x1 . How can such a potential difference be tested and estimated statistically?
Years of Work Experience and number of Job Offers of 10 job-seekers were as follows: Work Exp. 4 2 5 3 7 12 2 5 4 9 No. of Offers 7 1 8 4 13 19 3 11 9 15 a. Fit the regression equation of No. of Job Offers on Years of Work Experience. b. What will be the predicted number of offers for an applicant with 6 years of experience? c. Verify the relationship between the number of job offers and years of work experience using at least two relevant methods
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2for a sample of N=20N=20 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.02. X1X1 X2X2 YY 31.4 32.3 25.2 85.4 28.1 53 66.3 42.6 67.4 59 56.1 70.7 52.4 40.4 39.7 86.4 23.7 35 50.9 36.7 34.4 74.4 38 64.9 57.3 47.6 67.4 61.9 33.3 41.3 48.6 49.7 53.6 46.6 47.2 34.5 31.8 38.7 40.9 86 55 74 69.8 27.7 45.9 65.8 48.2 42.4 44.7 55.3 55.1 57.3 27 31.5 60.4 28.1 19.4 65.9 26 13.7 SSreg= SSres= R2= F= P-value = What is your decision for the hypothesis test? Reject the null hypothesis, H0:β1=β2=0 Fail to reject H0H0 What is your final conclusion? The evidence supports the claim that one or more of the regression coefficients is non-zero The evidence supports the claim that all of the regression…

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y	x	d
70	11	1
102	19	1
76	12	1
83	14	1
61	17	0
62	13	0
67	20	0
98	16	1
84	11	1
101	15	1
51	16	0
108	16	1
32	13	0
71	15	1
101	17	1
90	15	1
112	19	1
88	13	1
110	18	1
95	17	1
44	14	0
51	19	0
112	17	1
113	17	1
52	13	0
61	10	1
100	16	1
78	14	1
90	16	1
57	16	0
59	15	0
53	15	0
119	19	1
109	18	1
68	11	0
104	19	1
45	18	0
67	17	0
65	15	0
74	14	1

y	x	d
70	11	1
102	19	1
76	12	1
83	14	1
61	17	0
62	13	0
67	20	0
98	16	1
84	11	1
101	15	1
51	16	0
108	16	1
32	13	0
71	15	1
101	17	1
90	15	1
112	19	1
88	13	1
110	18	1
95	17	1
44	14	0
51	19	0
112	17	1
113	17	1
52	13	0
61	10	1
100	16	1
78	14	1
90	16	1
57	16	0
59	15	0
53	15	0
119	19	1
109	18	1
68	11	0
104	19	1
45	18	0
67	17	0
65	15	0
74	14	1

y	x	d
70	11	1
102	19	1
76	12	1
83	14	1
61	17	0
62	13	0
67	20	0
98	16	1
84	11	1
101	15	1
51	16	0
108	16	1
32	13	0
71	15	1
101	17	1
90	15	1
112	19	1
88	13	1
110	18	1
95	17	1
44	14	0
51	19	0
112	17	1
113	17	1
52	13	0
61	10	1
100	16	1
78	14	1
90	16	1
57	16	0
59	15	0
53	15	0
119	19	1
109	18	1
68	11	0
104	19	1
45	18	0
67	17	0
65	15	0
74	14	1