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how can we know that we have to ans this question in context of distance not by rate
Bismuth83
1. We are asked to fill in the blanks for 2 parts: "Among urban locations, there is a ___ correlation between the rate of large purchases and the rate of restaurant visits" and "The range of the rate of restaurant visits is least for ___ locations".



2. Part 1. Let's mark all the urban locations and draw an estimated trend line. When the rate of large purchases increases, the rate of restaurant visits decreases. So, there is a negative correlation between the two.



3. Part 2. The range of the rate of restaurant visits in an area is the distance between the projection of the least and largest points (from that area) on the y-axis. The smallest range is the smallest distance. If we try to draw this out, we can see that the distance for the urban areas is less than the suburban and rural areas. So, the range of the rate of restaurant visits is least in urban areas.

4. Our answer will be:

Among urban locations, there is a strongly negative correlation between the rate of large purchases and the rate of restaurant visits.

The range of the rate of restaurant visits is least for urban locations.

Attachment:
RestaurantGraph1.jpg
Attachment:
RestaurantGraph2.jpg
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In part 2 I use distance as a method of comparing the ranges, I'm not replacing rates with it. You could solve the problem without this interpretation, but it's easier to look at this way.

I hoped that helped!
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how can we know that we have to ans this question in context of distance not by rate
Bismuth83
1. We are asked to fill in the blanks for 2 parts: "Among urban locations, there is a ___ correlation between the rate of large purchases and the rate of restaurant visits" and "The range of the rate of restaurant visits is least for ___ locations".



2. Part 1. Let's mark all the urban locations and draw an estimated trend line. When the rate of large purchases increases, the rate of restaurant visits decreases. So, there is a negative correlation between the two.



3. Part 2. The range of the rate of restaurant visits in an area is the distance between the projection of the least and largest points (from that area) on the y-axis. The smallest range is the smallest distance. If we try to draw this out, we can see that the distance for the urban areas is less than the suburban and rural areas. So, the range of the rate of restaurant visits is least in urban areas.

4. Our answer will be:

Among urban locations, there is a strongly negative correlation between the rate of large purchases and the rate of restaurant visits.

The range of the rate of restaurant visits is least for urban locations.

Attachment:
RestaurantGraph1.jpg
Attachment:
RestaurantGraph2.jpg
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HarshZsssh
how can we know that we have to ans this question in context of distance not by rate

For part II,

We need the range of rate. This means we need 'Maximum value of rate - Minimum value of rate'

The minimum value of rate for rural regions (blue circles) is very low and maximum value is quite high so range will be high - about 0.7

The minimum value of rate for suburban (grey square) and urban (black triangle) regions is about the same but the maximum value of rate for suburban is very high (almost 1) so range will be higher for suburban regions.

Hence range is lowest for urban regions (about 0.4)

Select Urban
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Why does chain as an option exists in the second blank and graph - if it is not a location?
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I haven't seen the source question but if it's intentional then it would serve to add complexity.
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Why does chain as an option exists in the second blank and graph - if it is not a location?
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Part 1 :
correlation between the rate of large purchases and the rate of restaurant visits - urban locations - > STRONGLY NEGATIVE because we can see Black triangles as value on x-axis increases , value of y-axis decrease.

Part 2:
Range of the rate of restaurant visits, we know Range = Max - Mini
Rural : Range = 0.75 - 0.05 = 0.7
Sub Urban : Range = 1 - 0.3 = 0.6
Urban : Range = 0.7 - 0.3 = 0.4

Answer - Least is URBAN
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