Further the math conversation by commenting on the correlation between the two v

Question

Further the math conversation by commenting on the correlation between the two variables and why you believe the regression equation is a good or poor model for prediction.

I chose the Restaurants for this post and used Cost and Service for my variables to see if there is a link between cost and service. I will also attach the paper in case the picture of the scatter plot does not show up.

What is the linear regression (prediction line) equation? What is the coefficient of determination?

Y=0.0837x+16.072 R2= 0.42

Do you think that there is a strong positive or strong negative correlation? Why or why not? Is this result what you expected?

I think that there is a Weak Positive correlation the plot points have a somewhat wide disbursement but do head in an upward liner direction. Surprisingly, it shows that there are some restaurants out there that the service rate is higher even though the prices of the food is not very expensive, I have circled them in yellow.

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Location Cost Food Décor Service Summated Rating Coded Location Bins Midpoints Center City 29 20 13 18 51 0 9.99 15 Center City 29 22 14 18 54 0 19.99 25 Center City 88 26 25 25 76 0 29.99 35 Center City 58 24 17 23 64 0 39.99 45 Center City 29 22 17 16 55 0 49.99 55 Center City 62 20 19 21 60 0 59.99 65 Center City 64 24 24 22 70 0 69.99 75 Center City 65 22 23 22 67 0 79.99 85 Center City 54 25 22 22 69 0 89.99 95 Center City 29 22 16 18 56 0 99.99 Center City 36 24 15 20 59 0 Center City 78 22 22 19 63 0 Center City 45 20 18 17 55 0 Center City 40 21 19 19 59 0 Center City 67 24 23 22 69 0 Center City 49 24 20 17 61 0 Center City 33 21 18 19 58 0 Center City 83 25 20 22 67 0 Center City 76 24 23 25 72 0 Center City 63 22 18 22 62 0 Center City 29 20 15 16 51 0 Center City 32 21 12 21 54 0 Center City 60 23 23 20 66 0 Center City 22 21 13 18 52 0 Center City 40 21 14 19 54 0 Center City 63 21 24 22 67 0 Center City 45 22 14 20 56 0 Center City 56 23 20 22 65 0 Center City 76 24 23 20 67 0 Center City 64 24 23 21 68 0 Center City 50 17 21 19 57 0 Center City 99 22 25 21 68 0 Center City 48 20 15 19 54 0 Center City 56 23 20 21 64 0 Center City 34 22 11 19 52 0 Center City 59 21 20 20 61 0 Center City 69 18 24 19 61 0 Center City 53 27 15 21 63 0 Center City 71 25 15 23 63 0 Center City 69 23 16 20 59 0 Center City 35 23 13 19 55 0 Center City 56 19 22 19 60 0 Center City 40 21 12 17 50 0 Center City 75 25 24 24 73 0 Center City 43 22 16 18 56 0 Center City 93 25 21 23 69 0 Center City 46 24 19 20 63 0 Center City 72 23 27 22 72 0 Center City 95 27 26 27 80 0 Center City 57 24 22 23 69 0 Metro Area 63 27 19 22 68 1 Metro Area 62 21 16 18 55 1 Metro Area 30 22 15 17 54 1 Metro Area 51 23 19 22 64 1 Metro Area 58 23 15 19 57 1 Metro Area 47 25 20 22 67 1 Metro Area 36 20 15 18 53 1 Metro Area 26 21 15 17 53 1 Metro Area 14 21 9 15 45 1 Metro Area 25 23 17 20 60 1 Metro Area 38 26 18 20 64 1 Metro Area 43 22 16 20 58 1 Metro Area 22 21 15 19 55 1 Metro Area 44 22 21 21 64 1 Metro Area 44 20 19 20 59 1 Metro Area 23 22 12 16 50 1 Metro Area 39 24 20 21 65 1 Metro Area 32 23 17 20 60 1 Metro Area 29 19 13 17 49 1 Metro Area 25 24 12 17 53 1 Metro Area 52 22 20 21 63 1 Metro Area 47 22 18 21 61 1 Metro Area 44 21 18 21 60 1 Metro Area 59 21 18 18 57 1 Metro Area 21 22 16 18 56 1 Metro Area 31 22 16 18 56 1 Metro Area 43 23 15 21 59 1 Metro Area 53 26 19 23 68 1 Metro Area 53 21 19 20 60 1 Metro Area 25 20 16 19 55 1 Metro Area 52 26 22 22 70 1 Metro Area 54 22 18 18 58 1 Metro Area 26 22 18 23 63 1 Metro Area 49 25 21 22 68 1 Metro Area 48 24 20 22 66 1 Metro Area 29 21 17 18 56 1 Metro Area 31 22 22 18 62 1 Metro Area 36 23 19 20 62 1 Metro Area 31 22 8 15 45 1 Metro Area 54 24 21 20 65 1 Metro Area 29 24 13 19 56 1 Metro Area 41 23 17 20 60 1 Metro Area 26 23 16 19 58 1 Metro Area 21 23 12 15 50 1 Metro Area 36 25 22 24 71 1 Metro Area 24 24 14 18 56 1 Metro Area 33 23 24 20 67 1 Metro Area 50 26 19 22 67 1 Metro Area 68 27 27 26 80 1 Metro Area 37 26 18 22 66

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Explanation / Answer

There is weak positive correlation between the predictor amd response variables.

The model is a poor fit since the coefficient of determination is 0.42 i.e. merely 42% which is very low.

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