# Multiple Regression

#### sandy7735

##### New Member
I would like to ask for some help. Completed a Pearson correlation testing 3 hypotheses. 2 of the R showed negative correlations and one a positive correlation. I wanted to follow up with a multiple regression test. My professor questions if multiple regression is appropriate because of the mix direction of the predictor variables. I am not finding anything that says it is appropriate or not, and if not, what sort of regression is advised?
Thanks in advance for help.

#### ondansetron

##### TS Contributor
Which is the outcome/dependent variable (what are you trying to predict)? How is it measured?

What variables do you think help explain/predict/influence that outcome variable? How are they each measured?

What is your sample size?

Multiple regression may be a reasonable option, but knowing more on your project will be helpful.

#### sandy7735

##### New Member
Thanks for your response.
1. My study concerns the perception of diffusion of healthcare software and how it related to hours of use.
2. 82 respondents completed surveys focusing on 4 domains. Each domain is represented by 7-8 questions. The likert-scale responses for the 7-8 questions were summed. A pearsons r correlation was applied.
3. 2 of the pearson r correlations resulted in signficant, negative correlations, 1 resulted in a signicant, positive correlation and there was not correlation in the 4th.
4. I want to ensure I am using the right regression model. If I have mixed predictors, does this preclude use of the the multiple regression model
5. My end goal is to determine which of the variables is best for predicting hours of use.

#### GretaGarbo

##### Human
In a multiple regression model some coefficients can be positive, some negative and some close to zero.

And the multiple regression coefficients can have different signs to the correlation coefficients.

#### sandy7735

##### New Member
In a multiple regression model some coefficients can be positive, some negative and some close to zero.

And the multiple regression coefficients can have different signs to the correlation coefficients.
Thank you for your response. So likely this is obvious to you, my next question concerns can you graph out a multiple regression when there are multiple independent variables? I have 4 independent variables that have different values and one dependent variable. I am trying to imagine this on a 2 dimensional graph.

#### ondansetron

##### TS Contributor
Sorry, it wasn't clear to me: which single variable are you trying to predict?

Also, yes, sorry I wasn't clear-- as @GretaGarbo said, the signs of coefficients within a model (pos/neg) do not restrict you from using the model.

As far as graphing a multiple regression, you can absolutely do that, you just need to set the other variables fixed at some values that may be important.

Lets take a simple example of E(Y) = f(x1, x2) = b0 + b1x1 + b2x2

If we want to graph the relationship of y and x1, we simply plug in some constant for x2 (lets do the number 1 for example), then you can see what happens:

E(Y)= b0 + b1x1 + b2*(1) = (b0 + b2) + b1x1

so now b0+b2 has become a constant for when x2 is fixed at 1, so we can see how Y changes with X1 when X2 is set to 1. If you have X3, X4, and so on, the process is similar. You may want to have them fixed at important values, say, the median for each X.

To visualize this, go grab a cutting board in your kitchen (or a piece of paper). with the thin edge toward you, this is one single line. Now rotate the sheet/board so the flat broad side is facing you and perpendicular to the ground. If you imagine parallel lines across this surface, this is how the model might visualize for the above situation of parallel lines (no interaction). If you want to show interaction, look at the following image:

Image from google if that helps.

#### sandy7735

##### New Member
Many thanks to all for your help

#### noetsi

##### Fortran must die
There is dispute if likert scale is ordinal or interval like. If its ordinal (if the dv is ordinal) then linear regression is not an appropriate method.

#### AliH

##### New Member
Can someone please help me in these questions, I just need a clue for the questions!

Better Blooms is a florist shop which takes orders by internet and phone, prepares the desired floral arrangements, and delivers within a 25-mile radius of the shop. Since the profit margin on the business is small for each arrangement and the competition from other florists in the area is high, the owner is concerned about setting the appropriate costs for each delivery to be profitable while still being competitive. To investigate, the owner has gathered information on a random sample of 50 recent orders and has asked you to analyze the data using statistical methods and to report to her your findings. Factors thought to be related to the cost of delivering a floral arrangement are thought to be: (1) Preparation Time – the time in minutes between when the customer has placed an order and when it is ready for delivery; more expensive arrangements take longer to prepare, (2) Delivery Time – the travel time in minutes from the shop to the recipient of the arrangement, and (3) Mileage – the distance in miles from the shop to the customer (mileage and delivery time are sometimes inversely proportional when the delivery truck can use an interstate instead of traveling through heavy downtown traffic, for instance).