Question

Due on August 02, 2018 Name: Na Na Name: ID ID ID Q1. A random sample of two variables, x and y, produoed the following observations 42 3 253537 3H 31 33 19238 2829 361 8 6 I. Write the regression model. 2. Determine the regression line . What does the coefticient bl tell you. 4. Use the regression equation to determine the predicted values of y and calculate the residuals Calculate the sum squares residuals 6. Calculate the standard error of estimate. 7. Determine the coefficient of determination Interpret the R' Plot the residuals against the predicted values of y. What does the graph tell you? 10. Test to determine whether the population correlation coefficient is positive. Use a significance level of 0.0S for the hypothesis test.

solve problems ( 8,9 &10)

Answer 1

we can run the regression analysis in excel by going to data > data analysis tab and selecting regression

The r2 value is 0.7677

this means that the model is able to explain 76.77% varaition in the value of Y due to variation in the values of X

The correlation coefficient is
0.8761

hence this is a positive correlation on the higher side

please note that correlation can take values from -1 to 1 , with values near zero indicating weak correlation , negative values indicate a negative correlation

the residual plot is

looks like some information is still left from the data to be extracted as the residuals form a wavy pattern , ideally we should not be able to see any pattern in the residual graph

There are 15 data points
hence the df is this case is

df = n-2 = 13

now we check the correlation table to check for the critical value at df = 13 and alpha = 0.05

the value is 0.514 , please see the correlation table for this

as the correlation value is greater than this critical value hence we conclude that the correlation value is signficant