The following data represent a set of 10 experimental runs in which two independent variables X1 and X2 are controlled and values of a response Y are observed: Y 61.5 61.2 32 52.5 31.5 22.5 53 56.8 34.8 52.7 52.53 Estimate the multiple Linear regression, Y = a + b₁ X₁ 1. The regression estimate a. 55.23 1.68 X1 2400 2450 2500 2700 2750 2800 2900 3000 3100 3200 004 X2 54.5 56.4 43.2 65.2 45.5 47.5 65 66.5 57.3 68

The following data represent a set of 10 experimental runs in which two independent variables X1 and X2 are controlled and values of a response Y are observed: Y 61.5 61.2 32 52.5 31.5 22.5 53 56.8 34.8 52.7 52.53 Estimate the multiple Linear regression, Y = a + b₁ X₁ 1. The regression estimate a. 55.23 1.68 X1 2400 2450 2500 2700 2750 2800 2900 3000 3100 3200 004 X2 54.5 56.4 43.2 65.2 45.5 47.5 65 66.5 57.3 68

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 1TU: The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t=...

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The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
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?
Consider the following sample regressions for the linear and quadratic models along with their respective R2 and adjusted R2. Linear Quadratic Intercept 13.3087 1.7656 x 0.3392 4.0966 x2 NA -0.2528 R2 0.1317 0.5844 Adjusted R2 0.0232 0.4657 Choose the model with the best fit, and then predict y for x = 4, 8, and 12. ROUND TO TWO DECIMAL PLACES. x Predicted y 4 8 12
Consider the following table of N=3 observations. Calculate estimates of b1 and b0 (b-hat) considering the linear regression model y=b+b*x Compute SSE for this regression Assume that SST=32. What is R^2 for this regression?
The accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter The predicted y-hat value for a diameter of 201 is 864. if we observed a weld that had a diameter of 235 that had a strength 1000, what would be its residual?
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.
For a sample of over 160 college students, the following variables were measured: Y = height X1 = mother’s height X2 = father’s height X3 = 1 if male, 0 if female The goal is to predict student’s height using the mother’s and father’s heights, and sex, where sex is categorized using the variable “male” = 1 if male, 0 if female. Question 1 The regression model is __________________________________________ Regress command results (remember that we now have n = 165 cases; we removed one outlier): Source | SS df MS Number of obs = 165 -------------+------------------------------ F( 3, 161) = 104.38 Model | 1679.17741 3 559.725803 Prob > F = 0.0000 Residual | 863.31653 161 5.36221447 R-squared = 0.6604 -------------+------------------------------ Adj R-squared = 0.6541 Total | 2542.49394 164 15.5030118 Root MSE = 2.3156…
Use the sample linear regression line Y^=2+3X for the data points below to answer the following questions. X 0 3 7 10 Y 5 5 27 31 1) What is the fitted value when X2=3? 2) What is the regression residual when X2=3?
A set of n = 15 pairs of X and Y values has a correlation of r = +0.80 with SSY = 75, and the regression equation for predicting Y is computed. Find the standard error of estimate for the regression equation. How big would the standard error be if the sample size were n = 30.
Which of the following does not need to be computed to determine a simple regression line? SSx SP "Y-hat" SSy
A new computer circuit was tested and the times (in nanoseconds) required to carry out different subroutines were recorded. Difficulty 1 3 3 4 5 6 6 6 Time 10 11 12 9 15 19 21 18 Find the regression line for the data. Assume x is the difficulty level and y is the time. (Round your values to four decimal places.)
For each of the following, explain what is wrong and why. a)In simple linear regression, the null hypothesis of the ANOVA F test is H0: β0 = 0. b)In an ANOVA table, the mean squares add. In other words, MST = MSM + MSE. c)The smaller the P-value for the ANOVA F test, the greater the explanatory power of the model. d)The total degrees of freedom in an ANOVA table are equal to the number of observations n.