a) Find the value of the line ar correlation coefficient rb) Find the critical values ofr from table A-6 using x= 0.05c) Determine whether there is sufficient evidence to support a claim of a linear correlationBetween the two variables.d) Find the regression equation,e) Letting the first variable be the predictor (x) variable, find the indicated predicted value. Q4. Using the listed duration and interval after times, find the best predicted “interval after"time for an eruption with a duration of 253 seconds. How does it compare to an actual eruptionwith a duration of 253 seconds and an interval after time of 83 minutes?Duration 242255227251262207140Interval918191921029491After

Given the data; Duration(X) Interval After(Y) XY X2 Y2 242 91 22022 58564 8281 255 81 20655 65025 6561 227 91 20657 51529 8281 251 92 23092 63001 8464 262 102 26724 68644 10404 207 94 19458 42849 8836 140 91 12740 19600 8281 1584 642 145348 369212 59108 a) Correlation coefficient is given by- r=n(∑xy)-(∑x)(∑y)[n∑x2-(∑x)2][n∑y2-(∑y)2]=7×145348-(1584×642)7×369212-(1584)27×59108-(642)2=50875428×1592=50810958.1648r=0.0463 b) The critical value of r from table using α=0.05 is 0.754. Since the observed r value is less than the critical value hence it is not significantly different.c) Null and alternative hypothesis is- H0:r=0Ha:r≠0α=0.05 Test statistic is- t=rn-21-r2 Substituting values, we get; t=0.04637-21-0.04632=0.10350.9989=0.1036 P-value is the probability of obtaining the test statistics. Hence p-value at7-2=5 degree of freedom is 0.9215. Since this p-value is greater than the significance value of 0.05, we will accept the null hypothesis and will conclude that there is insufficient evidence to say that there is a significant linear relationship between duration and interval after.d) To find the regression equation- Interval After= Intercept + Slope*Duration Slope is calculated as- Slope=n∑xy-(∑x)(∑y)n∑x2-(∑x)2=7×145348-(1584×642)7×369212-(1584)2=50875428=0.0067 Intercept is given by- Intercept=∑y-b∑xn=642-0.0067×15847=90.1981 Regression equation is given as- Interval After=90.1981+0.0067*Duration e) To predict Interval after with a given duration of 253 seconds is- Interval After=90.1981+0.0067*253=91.8932

Math

Statistics

a) Find the value of the line ar correlation coefficient r b) Find the critical values ofr from table A-6 using x= 0.05 c) Determine whether there is sufficient evidence to support a claim of a linear correlation Between the two variables. d) Find the regression equation, e) Letting the first variable be the predictor (x) variable, find the indicated predicted value.

a) Find the value of the line ar correlation coefficient r b) Find the critical values ofr from table A-6 using x= 0.05 c) Determine whether there is sufficient evidence to support a claim of a linear correlation Between the two variables. d) Find the regression equation, e) Letting the first variable be the predictor (x) variable, find the indicated predicted value.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

100%

a) Find the value of the line ar correlation coefficient r
b) Find the critical values ofr from table A-6 using x= 0.05
c) Determine whether there is sufficient evidence to support a claim of a linear correlation
Between the two variables.
d) Find the regression equation,
e) Letting the first variable be the predictor (x) variable, find the indicated predicted value.

Q4. Using the listed duration and interval after times, find the best predicted “interval after"
time for an eruption with a duration of 253 seconds. How does it compare to an actual eruption
with a duration of 253 seconds and an interval after time of 83 minutes?
Duration 242
255
227
251
262
207
140
Interval
91
81
91
92
102
94
91
After

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