stats test tomorrow

Musa is interested in the relationship between hours spent studying and caffeine consumption among students at his school. He randomly selects 20 students at his school and records their caffeine intake (mg) and the amount of time spent studying in a given week. Here is computer output from a least squares regression analysis on his sample:

0. 164 plus/minus 2. 101 (0. 057)

Sophie wanted to know if sons of taller fathers tend to be taller. She collected data about the heights of a random sample of 110 men and about their fathers' heights. Here is computer output from a least-squares regression analysis on her sample:

0.431 plus/minus 1.66(0.059)

AccordingtotheUNSDG2report,howmanypeopledonothaveregularaccess to safe, nutritious food?

2 billion people

Whatintervalbestreflectsthepercentageoftheworld'spopulationthatis currently affected by hunger?

9.2-9.8

2. What does a negative correlation coefficient indicate?

A negative relationship between the variables

6. Which type of relationship does a positive slope in a scatter plot indicate?

A positive correlation

Which of the following best describes a confidence interval?

A range of values that estimates the population parameter with a specified level of confidence.

7. What does an outlier represent in a scatter plot?

Anomalies in the data

What do high-leverage points represent in a regression model?

Data points that have a significant impact on the regression line

Cam tracked how much toothpaste he used (in mg) and how long he brushed his teeth (in seconds) for a random sample of brushings. He saw a positive relationship between the amounts and times. A 95% confidence interval for the slope of the regression line was 0. 38 ± 0. 56. Cam wants to use this interval to test 𝐻0: β = 0 vs 𝐻𝑎: β ≠ 0 at the α = 0. 05 level of significance. Assume that all conditions for inference have been met. Which of these is the most appropriate conclusion about Cam's brushing habits?

Fail to reject 𝐻0. Cam can't conclude a linear relationship between how much toothpaste he uses and how long he brushes. (The interval estimating the slope β contains 0, so he can't reject 𝐻0: β = 0.)

WhataretwofactorsthatMs.Lariosmentionedthatimpactone'ssusceptibilityto living in a state of hunger?

Geographicallocationandsocioeconomicstatus

3. What do clusters represent in a scatter plot?

Groups of data points close together

When interpreting the coefficient of an independent variable in a regression model, which statement is correct?

It represents the correlation between the independent and dependent variables.

Which of the following assumptions is NOT required for linear regression?

Multicollinearity

Leonard took a random sample of his recent text messages and found a positive linear relationship between how many minutes he took to reply and how many minutes the other person took to reply. Here is computer output from a least-squares regression analysis on his sample: Leonard wants to test 𝐻0: β = 0 vs 𝐻𝑎: β ≠ 0. Assume that all conditions for inference have been met. At the α = 0. 05 level of significance, is there sufficient evidence to conclude a linear relationship between these variables in Leonard's text messages? Why?

NO, since 0. 168 > 0. 05 Since P-value associated with the slope is greater than the significance level, there's not enough evidence to conclude 𝐻𝑎.

8. What does a correlation coefficient of 0 indicate?

No correlation between the variables

4. How is the correlation coefficient measured?

On a scale of -1 to 1

Whatisonewaywecangetinvolvedtoattacktherootcausesofhunger, according to Ms. Larios?

Support small farmers

In multiple linear regression, what does the term "multicollinearity" refer to?

The presence of strong correlations among independent variables

What does the alpha level represent in hypothesis testing?

The probability of making a Type I error

What does the coefficient of determination (R-squared) measure in regression analysis?

The proportion of variance in the dependent variable explained by the independent variable(s)

1. What does the slope of a regression line represent?

The rate of change of the response variable for a one-unit change in the explanatory variable

8. What does a P-value of 0.03 mean in the context of a hypothesis test?

There is a 3% chance of obtaining the observed results, or more extreme, if the null hypothesis is true. A p-value represents the probability of observing results at least as extreme as those in your study, given that the null hypothesis is true ; it does not directly indicate the probabilities of hypotheses being true or false nor does it represent error rates after decisions are made.

What is the primary objective of regression analysis?

To estimate the parameters of a mathematical model that describes the relationship between variables

What is the purpose of residual analysis in regression?

To identify outliers in the data

Miles runs a website where users get points for posting content and points for commenting on others posts. He took a random sample of users and found a positive linear relationship between their post points and their comment points. Here is computer output from a least-square regression analysis on this sample: Regression: Comment Points VS Post Points Miles wants to test 𝐻0: β = 0 vs. 𝐻𝑎: β > 0. Assume that all conditions for inference have been met. At the α = 0. 05 level of significance, is there sufficient evidence to conclude a positive linear relationship between these variables for all users? Why?

YES, since 0. 000 < 0. 05 The two-sided P-value is approximately 0, and a one-sided P-value would be even smaller and certainly less than α = 0.05.Sothesampleslopeisunlikelytooccurbychancealone.Hehassufficientevidencetoconclude

8. Thereisnoeconomicburdenofeatinghealthierfoods.

false

A2,000caloriedietisconsideredstandardformostadults.Thedefining characteristic of SDG 2, Hunger, is not reaching that caloric intake.

false

Nkechi took a random sample of 10 countries to study fertility rate (babies per woman) and life expectancy (in years). She noticed a negative linear relationship between those variables in the sample data. Here is regression output on the sample data:

t= -5.973/0.587

Ona took a random sample of 20 soccer teams across Europe, and tracked the average number of goals each team scored per match, and how many total matches each team won, in the 2014 - 2015 season. Here is regression output on the sample data:

t= 14.02/1.15

Statisticscanbemisconstruedtopresentdatainanintentionallydeceptiveway.

true

TheUnitedStatesisoneofthefewUNcountriestonotconductavoluntary national review of the implementation of SDGs

true