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Regression Analysis and Hypothesis Testing, Exams of Mathematics

Princeton UniversityMathematics

Various topics related to regression analysis and hypothesis testing, including identifying outliers, determining linear correlation, calculating prediction intervals, estimating regression equations, and analyzing the relationship between variables. Several data sets and questions that require the application of statistical concepts and techniques to analyze the data and draw conclusions. The topics covered are relevant to fields such as statistics, data analysis, and applied mathematics, and the document could be useful for university students studying these subjects as study notes, lecture notes, or for exam preparation.

Typology: Exams

2024/2025

Available from 10/24/2024

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MATH302 WK7 TEST QUESTIONS WITH
ANSWERS
The least squares regression line for a data set is yห†= -4.6+1.56x and the standard
deviation of the residuals is .52
Does a case with the values x = -1.12, y = -8 qualify as an outlier? - .......ANSWERS ๐Ÿ”ท๐Ÿ–Š
โœ”โœ”Yes
The least squares regression line for a data set is yห†= -2.3โˆ’0.33x and the standard
deviation of the residuals is 0.26.
Does a case with the values x = -3.33, y = -1.27 qualify as an outlier? - .......ANSWERS
๐Ÿ”ท๐Ÿ–Šโœ”โœ”No
The following data represent the weight of a child riding a bike and the rolling distance
achieved after going down a hill without pedaling.
Can it be concluded at a 0.01 level of significance that there is a linear correlation
between the two variables? - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”yes, the p-value = .0055
The following data represent the weight of a child riding a bike and the rolling distance
achieved after going down a hill without pedaling.
Find the 95% prediction interval for rolling distance when a child riding the bike
weighs 106 lbs. (round to 4 decimal places)
___< y < ___ - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”39.3540 < y < 70.5679
The following data represent the weight of a child riding a bike and the rolling distance
achieved after going down a hill without pedaling.
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MATH302 WK7 TEST QUESTIONS WITH

ANSWERS

The least squares regression line for a data set is yห†= -4.6+1.56x and the standard deviation of the residuals is. Does a case with the values x = -1.12, y = -8 qualify as an outlier? - .......ANSWERS ๐Ÿ”ท๐Ÿ–Š โœ”โœ”Yes The least squares regression line for a data set is yห†= -2.3โˆ’0.33x and the standard deviation of the residuals is 0.26. Does a case with the values x = -3.33, y = -1.27 qualify as an outlier? - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”No The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling. Can it be concluded at a 0.01 level of significance that there is a linear correlation between the two variables? - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”yes, the p-value =. The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling. Find the 95% prediction interval for rolling distance when a child riding the bike weighs 106 lbs. (round to 4 decimal places) ___< y < ___ - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”39.3540 < y < 70. The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling.

Find the 99% prediction interval for rolling distance when a child riding the bike weighs 99 lbs. (round to 4 decimal places) ___< y < ___ - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”19.3556 < y < 69. Which of the following describes how the scatter plot appears? Select all that apply.

  • .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”Strong, Weak, Nonlinear The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Approximately what percentage of the variation in Kilowatts is accounted for by Temperature in this model? Place your answer, rounded to 1 decimal place, in the blank. Do not use any stray punctuation marks or a percentage sign. For example, 78.9 would be a legitimate entry. ___% - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”89. A company want to find out if there is a linear relationship between indirect labor expense (ILE), in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 25 months are given. Using that data, find the estimated regression equation which can be used to estimate ILE when using DLH as the predictor variable. - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”ILE = 171.
  • 9.3172(DLH) A company want to find out if there is a linear relationship between indirect labor expense (ILE), in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 25 months are given. Based on your results, If direct labor hours (DLH) increases by one hour, the indirect labor expense (ILE), on average, increases by approximately how much?

Based on your results, If the Colas Consumed increases by 1, Bone Mineral Density, on average, decreases by approximately how much? Round to 3 decimal places. Make sure you put a 0 in front of the decimal. - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”0. A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed. Find the y-intercept and slope for the regression equation using technology (you can copy and paste the data into Excel). Round answer to 3 decimal places. ลท=___+___x - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”y = 23.395 + 2.925x Bone mineral density and cola consumption has been recorded for a sample of patients. Let x represent the number of colas consumed per week and y the bone mineral density in grams per cubic centimeter. Assume the data is normally distributed. Approximately what percentage of the variation in Bone Mineral Density is accounted for by Colas Consumed in this model? Place your answer, rounded to 1 decimal place, in the blank. Do not use any stray punctuation marks or a percentage sign. For example, 78.9 would be a legitimate entry. ___% - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”28. Bone mineral density and cola consumption has been recorded for a sample of patients. Let x represent the number of colas consumed per week and y the bone mineral density in grams per cubic centimeter. Assume the data is normally distributed. Using that data, find the estimated regression equation which can be used to estimate Bone Mineral Density when using Colas Consumed as the predictor variable.

  • .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”Bone Mineral Density = 0.891716 - 0.002389(Colas Consumed)

You decided to join a fantasy Baseball league and you think the best way to pick your players is to look at their Batting Averages. You want to use data from the previous season to help predict Batting Averages to know which players to pick for the upcoming season. You want to use Runs Score, Doubles, Triples, Home Runs and Strike Outs to determine if there is a significant linear relationship for Batting Averages. You collect data to, to help estimate Batting Average, to see which players you should choose. You collect data on 45 players to help make your decision. x1 = Runs Score/Times at Bat x2 = Doubles/Times at Bat x3 = Triples/Times at Bat x4 = Home Runs/Times at Bat x5= Strike Outs/Times at Bat Approximately what percentage of the variation in Batting Average is accounted for by these 5 variables in this model? - .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”86.01% of variation in Batting Average is accounted for by Runs Score, Doubles, Triples, Home Runs and Strike Outs in this model. You decided to join a fantasy Baseball league and you think the best way to pick your players is to look at their Batting Averages. You want to use data from the previous season to help predict Batting Averages to know which players to pick for the upcoming season. You want to use Runs Score, Doubles, Triples, Home Runs and Strike Outs to determine if there is a significant linear relationship for Batting Averages. You collect data to, to help estimate Batting Average, to see which players you should choose. You collect data on 45 players to help make your decision.

5 = Severe Is there a significant linear relationship between these 3 variables and Fawn Count? If so, what is/are the significant predictor(s) for determining Fawn Count?

  • .......ANSWERS ๐Ÿ”ท๐Ÿ–Šโœ”โœ”Yes, Adult Count, p-value = 0.01188964 < .05, Yes, Adult Count is a significant predictor for Fawn Count. Annual Rain in Inches, p-value = 0.004661804 < .05, Yes, Annual Rain in Inches is a significant predictor for Fawn Count. Winter Severity, p-value = 0.00462881 < .05, Yes, Winter Severity is a significant predictor for Fawn Count.