absolutely need help immediately!!!!

Question

Given n=10, x=20, ∝=0.05: 

Based on the data the regression equation is given by

 y=67.3+1.07x, y=75.2 and r=.224. 

 Find the best predicted value for x. 

Answer 1

Hi Jasmine,

I'm happy to help you with this; however, I want to be sure I understand your question. You are asking what the best predicted value of x is based on your regression equation. Are you sure the question is asking for the best predicted value of x and not the best predicted value of y? I ask this because in a regression equation, y is your dependent variable and x is your independent variable. In other words, the regression equation (or model) tells you about the relationship between the response variable y and the predictor variable x. The goal of regression is to predict y from x using a linear relationship (i.e., line of best fit). The variable for which we find the prediction is always y because it's what comes out of our regression equation.

To find the best predicted y value given a particular value of x, you can either use the regression equation or the mean of the y values. Although using the regression equation is preferred, you only want to use it if it is a good model because if it's not, there's no correlation between the variables (y and x). Based on your data, you see that your correlation coefficient is 0.224, which isn't very good and suggests the regression equation isn't very good. But, you can also find this objectively by using this table (https://www.statisticssolutions.com/table-of-critical-values-pearson-correlation/) to find the critical R-value, which you can then compare with the r value from your data (.224).

When you look at the table from in the link, the column on the far left is your sample size, or N. From your data, N=10, so if you look down the N column and find 10. Your alpha level is 0.05, which is the third column from the left. Starting at 10 under the N column, read across the row to find the number that falls under the 0.05 column - and you see that your correlation coefficient (r) is 0.576, which is more than the r-value from your data (0.224). This means there is no correlation between your variables and the regression model should not be used to make predictions. Instead, you should use the mean (average) of the y-values. To do so, calculate the mean y-value - this is your best predicted value.

If this doesn't make sense, please let me know and I'd be happy to work with you.