Data was gathered on the amount of rainfall X (in inches) for the last 5 years to analyze if the amount of rainfall X (in inches) could be used to predict the acorn output Y (in tons) for a group of oak trees. Researchers expect the the acorn output to increase linearly with the increase in rainfall amount. That is, they are specifically interested in testing if the correlation between the rainfall and the acorn output is positive (i.e.: ) . When the necessary conditions are satisfied, under the null hypothesis, test statistic for above test Group of answer choices follows a t distribution with degrees of freedom (n-1) follows a chi-square distribution with degrees of freedom (n-1) follows a t distribution with degrees of freedom (n-2) follows a standard normal distribution. follows a chi-square distribution with degrees of freedom (n-2)

A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ=140+5 mg/dl and σ=5+1 mg/dl. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured: Once? n=5+2 times n=5+4 times Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.

Low-Density Lipoprotein (or LDL) is considered the "bad" cholesterol because it forms plaques in arteries, raising the risk for heart attack and stroke. Suppose you are interested in predicting LDL (in mg/dL) using one's age (in years). Assume that LDL levels and age are normally distributed and that the correlation between the two variables is 0.534. Based solely on the regression effect, a person whose age is at the 60th percentile is predicted to have an LDL level ____. [Source: Ldl cholesterol: Definition, risks, and how to lower it. (2020, March 09). Retrieved from https://www.webmd.com/heart-disease/ldl-cholesterol-the-bad-cholesterol]    Question 4 options:   A)  above the 60th percentile   B)  exactly at the 60th percentile   C)  exactly at the 40th percentile   D)  I need more information to answer this   E)  below the 60th percentile

The consumption function captures one of the key relationships in economics. It expresses consumption as a function of disposal income, where disposable income is income after taxes. The attached file "Regression-Dataset1" shows data of average US annual consumption (in $) and disposable income (in $) for the years 2000 to 2016. a)what is the Pearson correlation value between income and consumption? Select one: Ⓒa. 0.978 b. 0.109 c. None of the above d. 0.791

discuss how the coefficient of determination and the coefficient of correlation are related and how you would use them in regression analysis

Suppose the correlation between height and weight for adults is +0.40.What proportion (or percent) of the variability in weight can be explained by the relationship with height?

What is a covariate?

Hello! Please analyse the table 3 and 4 in the image attached. the data is supposed to see if there is a relationship between the prevalence of obesity(table3) or life expectancy (table4) between males and females.  thank you!

A researcher is studying the intensity of hurricanes that entered the Gulf of Mexico between 1975-2015 and the average water temperature of the Gulf of Mexico at the hurricane's peak strength. What is the independent and dependent variable in this study?

An observational study is conducted to investigate the association between age and total serum cholesterol. The correlation is estimated at r = 0.35. The study involves n = 125 participants. The mean (std dev) age is 44.3 (10.0) years with an age range of 35 to 55 years, and mean (std dev) total cholesterol is 202.8 (38.4).   a) Estimate the equation of the line that best describes the association between age (as the independent variable) and total serum cholesterol.   b) Estimate the total serum cholesterol for a 50-year old person.    c) Estimate the total serum cholesterol for a 70-year old person.