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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.
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- (A) The linearity between two variables X and Y, in pairs, defined as X=[4,2,3,5,2,4] and Y=[6,4,6,8,5,10] is equal to? (B)An outbreak of certain illness was attributed to ice creams produced at a certain factory. Scientists measured the level of the illness causing factor in 10 randomly sampled batches of ice cream. The levels were: 0.583, 0.242, 0.129, 0.691, 0.231, 0.693, 0.619, 0.392, 0.418. What is the estimated interval of population mean at 0.05 level of significance? (C) The population standard deviation for the age of a certain University students is 13 years. If we want to be 90% confident that the sample mean age is within 3 years of the true population mean age of the University students, then how many randomly selected students must be surveyed?You have been presented with the following data and asked to fit statistical demand functions: PERIOD QUANTITY PRICE INCOME ADVERTISING 1 120 8.00 10 3 2 165 4.00 22 7 3 120 7.00 20 5 4 165 3.00 20 8 5 180 4.00 30 8 6 90 10.00 19 6 7 150 4.00 18 10.2 8 190 1.60 25 9.3 9 160 5.00 30 8 10 200 2.00 35 9.5 Non-linear relationship. Select and estimate any form of non-linear relationship. Is the estimated demand function “good”? Why or why not? Compare with the linear form above. Elaborate.1. Prior to being hired, the ve salespersons for a computer store were given a standard sales aptitude test. For each individual, the score achieved on the aptitude test and the number of computer systems sold during the first 3 months of their employment are shown in the attached image. (a) Determine the least-squares regression line and interpret its slope. (b) Estimate, for a new employee who scores 60 on the sales aptitude test, the number of units the new employee will sell in her first 3 months with the company. (c) Find the standard error of estimate. (d) Find the r-square of the model.
- Refer image to questions -What are the degrees of freedom? (choose from below) 45 43 71 47 - What is the correct decision for this test? (choose from below) Since p-value > 0.05, do not reject H0 Since p-value < 0.05, reject H0 Since p-value > 0.05, reject H0 Since p-value < 0.05, do not reject H0 - An appropriate conclusion for this test is (choose from below) -There is a significant positive linear relation between the first and second pulse rates of those who did not run on the spot -There is a significant negative linear relation between the first and second pulse rates of those who did not run on the spot -There is no significant linear relation between the first and second pulse rates of those who did not run on the spot -There is not enough evidence of a linear relation between the first and second pulse rates of those who did not run on the spotConsider the following variables: Y=daily productivity score (measured in points) X1=0 if undergraduate student,1 if graduate student X2=hours of sleep per night 1. If you want to test whether type of student modifies the association between hours of sleep per night and daily productivity score, which model (from attached image) should you consider and what is the null hypothesis for this test? A. Use Model 3 and test H0: β2=0 B. Use Model 5 and test H0: β3=0 C. Use Model 5 and test H0: β1=0 D. Use Model 5 and test H0: β2=0 E. Use Model 2 and test H0: β1=0 2. Suppose that you decide to use Model 5 (from pocture attached) to describe the relationship between type of student, hours of sleep per night, and daily productivity score. You use the method of least squares to obtain the following: Y= -0.5 + 3(X1) + 1.5(X2) + 2.5(X1X2) What is the estimated slope relating hours of sleep per night and daily productivity score among undergraduate students? A. 2 B. None of…The relationship between the independent variable (IV) and the dependent variable (DV) is likely to be mediated by a third variable (MV). With regard to the statement above, which of the following is most likely to be correct? A IV = Students’ performance (i.e., marks) in the formative assessment; DV = Students’ performance (i.e., marks) in the summative assessment, and MV = Students’ level of comfort with the venue of the assessments B IV = Students’ performance (i.e., marks) in the summative assessment; DV = Students’ performance (i.e., marks) in the formative assessment, and MV = Students’ level of preparation for the assessments. C IV = Students’ performance (i.e., marks) in the formative assessment; DV = Students’ performance (i.e., marks) in the summative assessment, and MV = Students’ level of preparation for the assessments D IV = Students’ performance (i.e., marks) in the summative assessment; DV = Students’ performance (i.e., marks) in the formative assessment,…
- a. In a left-tailed test, α=.05, the critical value of z is:-1.645-1.962.33-2.58 b. The ____________ is the same as the point-slope form equation of a line, that is used for prediction.trendlineregression linefrequency polygonnone of thesec. If two variables are significantly correlated, we can predict the value of the dependent variable if we know the value of the independent variable. The process is called _______correlation analysishypothesis testingregression analysisestimationd. Involves two variables that are taken from a sample or population.univariate databivariate datahypothesisestimatee. For the decision rule: Reject the null hypothesis if the computed statistic _______ positive critical value or if the computed value statistic is ______ negative critical value.≥ ; ≤> ; <= ; <> ; =f. An intelligent guess about the characteristic of a population is calledmeanproportionhypothesistest statisticA dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows. Number ofAssemblers One-HourProduction (units) 2 15 4 25 1 10 5 40 3 30 The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. Click here for the Excel Data File Draw a scatter diagram. On the graph below, use the point tool to plot the point corresponding to the first Number of Assemblers and her Production (No of Assemblers1). Repeat the process for the remainder of the sample (No of…
- The scatterplot of these two variables reveals a potential outlying month when the average temperature is about 53◦F and average crawling age is about 28.5 weeks. (a) Does this point have high leverage? (b) Is it an influential point?The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, 2 employees were assigned to assemble the subassemblies. They produced 11 during a one-hour period. Then 4 employees assembled them. They produced 18 during a one-hour period. The complete set of paired observations follows. Number ofAssemblers One-HourProduction (units) 2 11 4 18 1 5 5 23 3 18 The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. Click here for the Excel Data File Draw a scatter diagram. On the graph below, use the point tool to plot the point corresponding to the first Number of Assemblers and her Production (No of Assemblers1). Repeat the process for the remainder of the sample (No of Assemblers2,…One hundred individuals, aged 20-58, were given a test of psychomotor skill. Both age and score were classified in the accompanying table. Age High Ave Low 40 - 59 23 20 17 20 - 39 18 12 10 Test for dependency of the scores obtained in the psychometric test and the individual’s age. Set alpha at 5% level. State your hypothesis and show your solution and state your final conclusion.