100 adults from Coachella were randomly selected to participate in a study on the correlation between height in cm and weight in kg. Their heights had a range of 133 to 194 cm and their weights had a range from 38 to 150 kg. the 100 paired measurements had an average height of x bar= 167.87 and a weight average of ybar = 81.57. Also, relevant values between the two were r= 0.292, the p-value was 0.003 and y hat was 102+1.05x. Find the best predicted value y hat for the weight of someone who is 180cm all. Use a 0.1 significance level. We Can or cant use the regression equation ere? What would that estimate their weight to be?
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.
100 adults from Coachella were randomly selected to participate in a study on the
We Can or cant use the regression equation ere?
What would that estimate their weight to be?
Note:
Hi there! Thank you for posting the question. It seems that the question has some incorrect information. That is, the regression equation of y^ = 102 + 1.05x does not seem to be correct, because from this equation most of the values of the weights will range outside 150 kg. This does not estimate the weights between the range 38 to 150kg, so we have solved the question for you by taking the regression equation y^ = -102 + 1.05x. If you have any other value of regression equation, please re-submit the question by specifying the correct information.
Test whether the regression is significant or not:
Simple linear regression model:
A simple linear regression model is given as y = b0 + bx, where y is the predicted value of response variable, and x be the predictor variable. The quantity b is the estimated slope corresponding to x and b0 is the estimated intercept of the line, from the sample data.
The dependent variable is weight.
The independent variable is height.
Denote β as the regression coefficient for the predictor variable height.
The null and alternate hypotheses are stated below:
Null hypothesis H0:
H0: β = 0
That is, the variable height is not significant in predicting the response variable weight.
Alternative hypothesis H1:
H1: β ≠ 0
That is, the variable height is significant in predicting the response variable weight.
Given that the regression model is:
Weight = 102 + 1.05Height.
The level of significance is α = 0.1.
Given that the P-value corresponding to the predictor variable height is P-value = 0.003.
Decision rule based on P-value approach:
If P-value ≤ α, then reject the null hypothesis H0.
If P-value > α, then fail to reject the null hypothesis H0.
Conclusion based on P-value approach:
The P-value is 0.003 and α value is 0.1.
Here, P-value is less than the α value.
That is, 0.003 (=P-value) < 0.1 (=α).
By the rejection rule, reject the null hypothesis H0.
Hence, at the 0.1 level of significance, there is sufficient evidence to conclude that the predictor variable height is significant in predicting the response variable weight.
Therefore, we can use the regression equation.
Step by step
Solved in 3 steps with 1 images
