A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The regression equation is given below, where x denotes seed density, and y denotes lawn quality. The correlation coefficient r = .600. y = 33.14 + 4.54x If possible, use the information to obtain an estimate of the mean lawn quality for all lawns sown with a seed density of 4.7 (assume 4.7 is within the domain of the observed seed densities). Pay attention to all details before choosing your answer of the 4 below. Choices: A.) Since the correlation coefficient, r, is less than rcrit = 0.707, the correlation is significant and the lawn quality estimate is 54.48. B.) Since the correlation coefficient, r, is less than rcrit = 0.632, the correlation is not significant and therefore no estimate can be made. C.) Since the correlation coefficient, r, is less than rcrit = 0.632, the correlation is significant and the lawn quality estimate is 54.48. D.) Since the correlation coefficient, r, is less than rcrit = 0.707, the correlation is not significant and therefore no estimate can be made.
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.
A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The regression equation is given below, where x denotes seed density, and y denotes lawn quality. The
y = 33.14 + 4.54x
If possible, use the information to obtain an estimate of the mean lawn quality for all lawns sown with a seed density of 4.7 (assume 4.7 is within the domain of the observed seed densities). Pay attention to all details before choosing your answer of the 4 below.
Choices:
A.) Since the correlation coefficient, r, is less than rcrit = 0.707, the correlation is significant and the lawn quality estimate is 54.48.
B.) Since the correlation coefficient, r, is less than rcrit = 0.632, the correlation is not significant and therefore no estimate can be made.
C.) Since the correlation coefficient, r, is less than rcrit = 0.632, the correlation is significant and the lawn quality estimate is 54.48.
D.) Since the correlation coefficient, r, is less than rcrit = 0.707, the correlation is not significant and therefore no estimate can be made.
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