A study reported by an electric engineering student considered the effect of X-ray inspection of integrated circuits. The radiation dose were studied as a function of current (in milliamps) and exposure time ( in minutes). The data are shown below. S.N 1 2 3 Radiation dose 4 5 6 7 8 9 10 Current 10 10 10 10 15 15 15 20 20 20 7.4 14.8 28.6 59.2 88.8 11.1 14.8 22.2 29.6 59.2 A: Simple Linear regression model between radiation dose and exposure time. Exposure time 0.25 0.5 1 2 3 10 15 0.5 1 2

A study reported by an electric engineering student considered the effect of X-ray inspection of integrated circuits. The radiation dose were studied as a function of current (in milliamps) and exposure time ( in minutes). The data are shown below. S.N 1 2 3 Radiation dose 4 5 6 7 8 9 10 Current 10 10 10 10 15 15 15 20 20 20 7.4 14.8 28.6 59.2 88.8 11.1 14.8 22.2 29.6 59.2 A: Simple Linear regression model between radiation dose and exposure time. Exposure time 0.25 0.5 1 2 3 10 15 0.5 1 2

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 4GP

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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?
The Update to the Task Force Report on Blood Pressure Control in Children [12] reported the observed 90th per-centile of SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of average height are given in Table 11.18. Suppose we seek a more efficient way to display the data and choose linear regression to accomplish this task. age sbp 1 99 2 102 3 105 4 107 5 108 6 110 7 111 8 112 9 114 10 115 11 117 12 120 13 122 14 125 15 127 16 130 17 132 Do you think the linear regression provides a good fit to the data? Why or why not? Use residual analysis to justify your answer. Am I supposed to run a residual plot and QQ-plot for this question?
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
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenueas a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly GrossRevenue($1000s) Television Advertising($1000s) Newspaper Advertising($1000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 a. Develop an estimated regression equation with the amount of televisionadvertising as the independent variable.b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. c. Is the estimated regression equation coefficient for television advertisingexpenditures the same in part (a) and in part (b)? Interpret the coefficient in each case. d. Predict weekly gross revenue for a week when $3500 is spent on television advertising and $1800 is spent on newspaper advertising.
Life insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below. Say how you know from the output that there actually is a significant linear relationship between a male customer’s age at death and his father’s age at death. State the value of the coefficient of Father’s Age (Death) and interpret this value in the context of the problem at hand.State the value of the coefficient of determination in the model and interpret this value in the context of the situation.
Life insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below Examine both the scatterplot and the correlation matrix provided above. Comment on the apparent relationship between the customer’s age at death and their father’s age at death in the plot. Explain how the information in the correlation matrix supports your conclusion
In an attempt to develop a model of wine quality as judged by wine experts, data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 17 wines, a model was created using the percentages of alcohol to predict wine quality. From the results of that regression, b1=0.4386 and Sb1=0.1141. a. At the 0.05 level of significance, is there evidence of a linear relationship between the percentage of alcohol and wine quality? b. Construct a 95% confidence interval estimate of the population slope, β1. b. The 95% confidence interval is __ ≤ β1 ≤ __ (Round to three decimal places as needed.)
A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results. Increase in advertising expenditure (%) 0 5 15 20 25 30 35 40 Increase in sales (%) 5 10 18 25 35 50 60 65 Determine the value of regressions coefficients and write down the simple linear regression model.
A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…
Define the ADL and GLS Estimators of Regression.
An experiment was carried out to observe the relationship between the time (Y) necessary for a vendor to supply a showcase in a store with sodas, and the boxes of product supplied (X), the information recorded is as follows (image) From the data: a. Get the fitted simple linear regression model b. Construct a scatterplot and discuss the result c. perform the analysis of variance. Thanks
The authors of a paper were interested in how the distance a deer mouse will travel for food is related to the distance from the food to the nearest pile of debris. Distances were measured in meters. The data and computer output are given below. Distance from Debris Distance Traveled 6.94 0.00 5.23 6.13 5.21 11.29 7.10 14.35 8.16 12.03 5.50 22.72 9.19 20.11 9.05 26.16 9.36 30.65 Simple Linear Regression Results: Dependent Variable: Traveled Independent Variable: Debris Sample size: 9 R (correlation coefficient) = 0.5657 R-sq = 0.32002088 Estimate of error standard deviation 8.670711 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept -7.6854587 13.332196 ≠ 0 7 -0.5764586 0.5824 Slope 3.2340908 1.7818117 ≠ 0 7 1.8150575 0.1124 a)What is the least squares regression line for the output given above? b) what is the predicted traveled distance given the distance from debris is 6.5 meters?