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StatisticsQ&A LibraryEach year a market research company surveys new car owners 90 days after they purchase their cars. This data is used to rate auto brands (such as Toyota and Ford) on quality and customer satisfaction. Suppose the following were the quality rating and satisfaction scores for 30 brands sold in the United States. Brand Quality Rating Satisfaction Rating Acura 64 814 Audi 80 863 BMW 76 849 Buick 74 792 Cadillac 58 826 Chevrolet 64 791 Chrysler 58 783 Dodge 58 790 Fiat 38 768 Ford 66 789 GMC 60 791 Honda 71 783 Hyundai 70 804 Infiniti 63 821 Jeep 43 762 Kia 72 791 LandRover 55 858 Lexus 76 844 Lincoln 65 835 Mazda 74 790 Mercedes-Benz 67 842 MINI 68 795 Mitsubishi 51 748 Nissan 63 786 Porsche 76 882 Scion 65 779 Subaru 78 766 Toyota 72 783 Volkswagen 67 796 Volvo 69 812 (a) Construct a scatterplot of y = satisfaction rating versus x = quality rating. A scatterplot has 30 points.The horizontal axis is labeled "x" and has values from 35 to 85. The vertical axis is labeled "y" and has values from 740 to 885. The points are plotted in an upward curved pattern starting in the bottom left corner of the diagram and ending in the upper right corner of the diagram.There is only a small amount of variation about the trend.A scatterplot has 30 points.The horizontal axis is labeled "x" and has values from 35 to 85. The vertical axis is labeled "y" and has values from 740 to 885. The points are plotted in an downward diagonal pattern starting in the upper left corner of the diagram and ending in the bottom right corner of the diagram.There is only a small amount of variation about the trend.A scatterplot has 30 points. The horizontal axis is labeled "x" and has values from 35 to 85. The vertical axis is labeled "y" and has values from 740 to 885. The points are plotted in a roughly increasing diagonal pattern starting in the bottom left corner of the diagram and ending in the upper right corner of the diagram.There is a large amount of variation about the trend.A scatterplot has 30 points.The horizontal axis is labeled "x" and has values from 35 to 85. The vertical axis is labeled "y" and has values from 740 to 885. The points are plotted in an upward curved pattern starting in the bottom left corner of the diagram, becoming more steep to the right, and reaching a maximum over approximately 66 on the horizontal axis. Moving to the right the points are plotted in a downward diagonal pattern ending in the bottom left corner.There is only a small amount of variation about the trend.How would you describe the relationship between x and y? There is a moderate negative linear relationship between quality rating and satisfaction rating. There is a strong negative linear relationship between quality rating and satisfaction rating. There is a strong positive linear relationship between quality rating and satisfaction rating. There is a curved relationship between quality rating and satisfaction rating. There may be a weak positive linear relationship between quality rating and satisfaction rating. (b) Calculate the value of the correlation coefficient. (Round your answer to three decimal places.) r = Interpret this value. There is no correlation between quality rating and satisfaction rating. There is a weak negative linear relationship between quality rating and satisfaction rating. There is a strong negative linear relationship between quality rating and satisfaction rating. There is a weak positive linear relationship between quality rating and satisfaction rating. There is a strong positive linear relationship between quality rating and satisfaction rating.Question

Asked Mar 24, 2020

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Each year a market research company surveys new car owners 90 days after they purchase their cars. This data is used to rate auto brands (such as Toyota and Ford) on quality and customer satisfaction. Suppose the following were the quality rating and satisfaction scores for 30 brands sold in the United States.

Brand

Quality Rating

Satisfaction Rating

Acura

64

814

Audi

80

863

BMW

76

849

Buick

74

792

Cadillac

58

826

Chevrolet

64

791

Chrysler

58

783

Dodge

58

790

Fiat

38

768

Ford

66

789

GMC

60

791

Honda

71

783

Hyundai

70

804

Infiniti

63

821

Jeep

43

762

Kia

72

791

LandRover

55

858

Lexus

76

844

Lincoln

65

835

Mazda

74

790

Mercedes-Benz

67

842

MINI

68

795

Mitsubishi

51

748

Nissan

63

786

Porsche

76

882

Scion

65

779

Subaru

78

766

Toyota

72

783

Volkswagen

67

796

Volvo

69

812

(a)

Construct a scatterplot of y = satisfaction rating versus x = quality rating.

A scatterplot has 30 points.The horizontal axis is labeled "x" and has values from 35 to 85. The vertical axis is labeled "y" and has values from 740 to 885.

The points are plotted in an upward curved pattern starting in the bottom left corner of the diagram and ending in the upper right corner of the diagram.

There is only a small amount of variation about the trend.

A scatterplot has 30 points.The horizontal axis is labeled "x" and has values from 35 to 85. The vertical axis is labeled "y" and has values from 740 to 885.

The points are plotted in an downward diagonal pattern starting in the upper left corner of the diagram and ending in the bottom right corner of the diagram.

There is only a small amount of variation about the trend.

A scatterplot has 30 points. The horizontal axis is labeled "x" and has values from 35 to 85. The vertical axis is labeled "y" and has values from 740 to 885.

The points are plotted in a roughly increasing diagonal pattern starting in the bottom left corner of the diagram and ending in the upper right corner of the diagram.

There is a large amount of variation about the trend.

A scatterplot has 30 points.The horizontal axis is labeled "x" and has values from 35 to 85. The vertical axis is labeled "y" and has values from 740 to 885.

The points are plotted in an upward curved pattern starting in the bottom left corner of the diagram, becoming more steep to the right, and reaching a maximum over approximately 66 on the horizontal axis. Moving to the right the points are plotted in a downward diagonal pattern ending in the bottom left corner.

There is only a small amount of variation about the trend.

How would you describe the relationship between x and y?

There is a moderate negative linear relationship between quality rating and satisfaction rating.

There is a strong negative linear relationship between quality rating and satisfaction rating.

There is a strong positive linear relationship between quality rating and satisfaction rating.

There is a curved relationship between quality rating and satisfaction rating.

There may be a weak positive linear relationship between quality rating and satisfaction rating.

(b)

Calculate the value of the correlation coefficient. (Round your answer to three decimal places.)

r =

Interpret this value.

There is no correlation between quality rating and satisfaction rating.

There is a weak negative linear relationship between quality rating and satisfaction rating.

There is a strong negative linear relationship between quality rating and satisfaction rating.

There is a weak positive linear relationship between quality rating and satisfaction rating.

There is a strong positive linear relationship between quality rating and satisfaction rating.

Step 1

**a. To construct a scatterplot of y = Satisfaction rating versus x = quality rating:**

Given data represents the values of quality rating and satisfaction rating for 30 brands sold in United States.

Denote the variable satisfaction rating as *y *and the variable quality rating as *x*.

EXCEL software can be used to draw a scatterplot for *y *= Satisfaction rating versus *x *= quality rating.

**Software Procedure:**

The step-by-step procedure to plot a scatter diagram using EXCEL software is given below:

- Open an EXCEL file.
- Enter the data of
**Satisfaction rating**in column*A*and name it as*y* - Enter the data of
**Quality rating**in column*B*and name it as*x* - Select
**Data**and go to**Insert tab.** - Select
**Scatter or Bubble chart > Scatter plot**. - Click
**OK**. - Right click on the scatterplot and click on
**Add trendline.**

The Scatterplot is shown below:

From the scatterplot it is observed that, the scatterplot has 30 points. The horizontal axis has *x *values from 35 to 85 and the vertical axis has *y *values from 740 t0 880. The points are plotted in a roughly increasing diagonal pattern starting in the bottom left corner of the diagram and ending in the upper right corner of the diagram. There is a large amount of variation about the trend.

Therefore, 3^{rd} option is correct.

Step 2

**Describe the relationship between x and y:**

From the scatterplot it is observed that, the points are plotted in a roughly increasing order. That is, the increasing in the values of the variable *x *increases the values of the variable *y. *But this increase is not ...

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