Sample Bivariate Data

x

y

2.39

7.85

1.33

2.91

6.53

17.53

3.76

23.94

2.04

9.91

7.05

18.87

8.17

13.99

4.19

11.30

9.46

31.35

4.27

28.64

1.08

2.34

2.48

5.69

1.09

-12.17

7.09

3.73

7.85

9.64

1.33

16.65

2.43

0.43

3.10

25.29

8.44

33.42

7.66

2.07

7.45

22.29

1.42

14.56

7.38

35.06

7.18

52.11

5.85

34.16

7.19

0.12

1.48

16.79

7.71

42.22

4.68

16.74

2.96

22.93

7.02

19.40

3.63

15.18

5.94

27.22

2.12

-15.45

0.63

4.20

9.66

26.93

6.70

25.41

4.83

18.97

2.80

27.36

6.53

26.82

3.28

7.04

1.66

4.88

8.12

20.06

6.42

15.10

6.12

41.96

5.34

9.58

1.39

-14.59

1.06

-2.42

6.78

21.76

5.87

17.65

3.48

8.22

0.20

9.02

3.80

3.89

9.29

26.01

6.25

30.10

3.31

14.77

8.84

27.49

5.53

11.82

0.31

3.51

2.30

-2.33

9.69

36.44

5.50

41.88

4.98

21.41

8.12

37.14

1.81

30.34

2.84

17.68

4.27

6.87

9.02

36.50

4.84

15.26

0.63

-3.81

8.01

25.21

3.23

15.52

5.70

19.54

8.30

25.70

2.35

9.08

3.96

11.35

4.81

24.44

9.18

17.61

8.41

17.61

9.56

34.07

7.11

16.98

3.86

2.74

3.40

-6.93

6.44

32.47

4.18

29.86

9.79

27.75

3.09

2.02

7.87

14.51

9.42

19.81

2.37

-0.13

9.83

36.05

6.23

10.97

2.38

1.28

7.82

20.29

5.12

6.44

1.61

11.39

4.25

10.46

3.24

22.35

0.69

12.69

4.58

8.10

0.75

1.68

4.07

15.02

7.42

22.21

5.96

13.34

4.16

23.14

4.32

9.49

5.85

24.84

1.36

3.69

0.92

9.15

9.87

29.38

7.61

22.45

3.27

-1.83

6.56

12.63

0.11

2.60

1.59

13.47

8.63

13.78

4.28

5.13

8.35

34.27

4.16

13.92

4.59

15.96

8.94

25.72

6.13

16.51

7.29

33.88

0.30

-9.25

2.90

16.77

1.97

-2.98

3.75

28.14

7.56

33.49

5.33

16.87

9.63

30.88

3.46

26.61

8.12

28.88

1.54

0.20

6.35

32.54

9.93

23.62

0.48

1.84

3.92

22.25

6.44

14.93

1.03

4.89

3.93

26.73

0.98

-2.17

0.26

19.34

2.98

16.40

2.72

12.69

6.10

14.60

4.22

17.68

1.79

11.03

8.12

36.27

2.61

18.39

1.92

-11.05

1.05

15.55

1.24

26.66

6.60

15.65

1.80

-0.38

0.23

-12.30

4.34

14.14

4.22

13.48

1.57

5.73

2.55

-2.74

3.52

9.83

4.92

17.10

4.87

8.54

6.47

18.29

0.52

17.84

7.11

24.86

0.23

-5.34

9.79

35.99

6.60

26.93

8.08

24.27

7.91

16.48

0.57

2.80

6.05

7.75

4.37

6.37

4.74

12.52

3.83

17.92

2.47

24.72

4.53

20.41

2.34

7.15

8.03

30.27

5.29

23.02

0.48

6.34

9.06

48.44

0.64

2.91

9.66

21.97

9.35

27.28

0.91

16.44

6.51

13.71

7.27

17.09

2.11

11.71

1.80

25.88

8.48

22.93

1.09

4.65

0.70

-15.03

8.41

20.04

3.90

13.93

1.70

7.84

0.20

-4.50

0.03

3.94

6.53

21.85

8.17

25.49

7.51

40.66

8.57

28.36

7.52

28.50

1.16

7.58

3.28

10.29

9.27

20.40

4.77

13.01

1.15

19.30

8.43

28.93

7.18

23.83

4.66

18.92

9.60

22.81

2.04

-2.56

9.85

13.96

5.12

26.63

5.74

12.88

2.02

21.92

1.58

5.41

4.32

11.75

7.05

10.98

5.15

23.70

9.39

35.62

3.80

13.68

5.94

33.30

8.19

28.82

6.25

20.04

0.26

-3.05

0.64

0.54

6.34

15.40

1.61

20.85

5.01

14.68

3.13

29.12

0.93

-6.67

4.79

12.45

5.19

15.90

1.75

6.54

2.69

6.26

1.38

15.68

5.75

17.34

1.47

6.31

2.21

-3.05

8.03

13.44

6.33

33.15

9.56

14.29

4.23

14.97

5.97

43.14

2.01

3.69

9.46

20.50

7.19

29.06

8.47

24.62

2.15

13.56

0.73

8.80

4.75

28.61

2.66

1.56

6.13

11.67

7.79

44.25

0.69

8.94

0.95

2.53

0.37

-1.09

5.40

13.44

3.89

22.48

2.44

21.12

5.40

15.28

3.48

3.89

4.85

9.16

9.54

39.05

7.24

35.67

9.40

33.74

0.40

5.89

0.14

-5.25

2.01

7.54

0.19

4.27

8.09

28.96

0.73

5.91

8.02

18.05

2.76

4.06

6.80

19.58

0.64

-7.55

4.14

4.43

4.83

9.17

5.31

16.70

2.83

-1.81

8.78

34.56

4.39

9.25

5.12

0.31

1.46

12.39

8.34

22.62

0.45

6.56

9.33

29.27

1.63

-15.12

9.35

30.89

3.08

5.45

4.00

19.93

1.52

1.93

3.18

9.58

5.28

19.17

3.59

5.95

2.32

11.44

7.61

41.26

4.73

16.88

7.04

17.54

6.21

20.99

4.12

14.68

8.12

31.71

6.09

29.71

7.68

41.62

5.03

26.47

5.84

24.29

2.33

8.72

8.64

33.95

9.65

34.50

9.96

35.04

4.59

5.61

2.44

9.69

3.34

4.87

3.19

16.14

3.27

39.79

7.22

31.03

8.67

21.93

1.76

24.95

3.04

12.51

3.97

29.82

2.64

8.45

9.86

19.98

0.67

27.93

9.41

18.60

9.14

19.83

8.64

27.05

9.30

19.72

9.22

46.95

0.59

14.34

7.44

50.89

6.04

22.56

1.79

16.94

7.93

37.68

0.16

-8.62

4.08

8.76

7.85

37.91

2.93

5.45

4.51

29.79

6.20

15.45

6.33

-0.68

1.97

-0.58

6.97

3.32

1.09

-3.21

1.66

17.68

5.26

13.54

1.36

0.68

9.05

21.40

2.94

10.83

0.64

12.71

3.64

6.75

8.58

26.61

0.23

13.75

6.01

19.64

0.98

8.76

0.67

-2.35

8.25

30.26

9.39

18.31

7.74

33.15

1.94

-12.77

2.87

6.09

0.75

3.03

6.27

8.97

3.64

18.89

0.66

0.97

4.64

21.24

5.25

20.27

7.69

38.49

6.78

8.77

7.66

35.23

3.53

26.01

6.60

30.92

1.62

16.12

9.88

29.26

2.10

14.16

8.68

33.73

1.41

11.27

4.27

7.52

2.18

17.15

5.10

18.76

3.17

5.29

3.09

11.42

2.06

-6.45

0.51

6.66

9.21

22.09

5.52

8.11

0.73

12.65

3.60

-1.68

1.73

-19.67

5.35

0.02

0.84

-7.27

9.26

43.90

2.48

-5.47

3.00

28.25

9.04

27.19

8.89

29.88

8.15

39.84

0.74

5.21

6.40

0.38

Sample Bivariate Data

x

y

2.39

7.85

1.33

2.91

6.53

17.53

3.76

23.94

2.04

9.91

7.05

18.87

8.17

13.99

4.19

11.30

9.46

31.35

4.27

28.64

1.08

2.34

2.48

5.69

1.09

-12.17

7.09

3.73

7.85

9.64

1.33

16.65

2.43

0.43

3.10

25.29

8.44

33.42

7.66

2.07

7.45

22.29

1.42

14.56

7.38

35.06

7.18

52.11

5.85

34.16

7.19

0.12

1.48

16.79

7.71

42.22

4.68

16.74

2.96

22.93

7.02

19.40

3.63

15.18

5.94

27.22

2.12

-15.45

0.63

4.20

9.66

26.93

6.70

25.41

4.83

18.97

2.80

27.36

6.53

26.82

3.28

7.04

1.66

4.88

8.12

20.06

6.42

15.10

6.12

41.96

5.34

9.58

1.39

-14.59

1.06

-2.42

6.78

21.76

5.87

17.65

3.48

8.22

0.20

9.02

3.80

3.89

9.29

26.01

6.25

30.10

3.31

14.77

8.84

27.49

5.53

11.82

0.31

3.51

2.30

-2.33

9.69

36.44

5.50

41.88

4.98

21.41

8.12

37.14

1.81

30.34

2.84

17.68

4.27

6.87

9.02

36.50

4.84

15.26

0.63

-3.81

8.01

25.21

3.23

15.52

5.70

19.54

8.30

25.70

2.35

9.08

3.96

11.35

4.81

24.44

9.18

17.61

8.41

17.61

9.56

34.07

7.11

16.98

3.86

2.74

3.40

-6.93

6.44

32.47

4.18

29.86

9.79

27.75

3.09

2.02

7.87

14.51

9.42

19.81

2.37

-0.13

9.83

36.05

6.23

10.97

2.38

1.28

7.82

20.29

5.12

6.44

1.61

11.39

4.25

10.46

3.24

22.35

0.69

12.69

4.58

8.10

0.75

1.68

4.07

15.02

7.42

22.21

5.96

13.34

4.16

23.14

4.32

9.49

5.85

24.84

1.36

3.69

0.92

9.15

9.87

29.38

7.61

22.45

3.27

-1.83

6.56

12.63

0.11

2.60

1.59

13.47

8.63

13.78

4.28

5.13

8.35

34.27

4.16

13.92

4.59

15.96

8.94

25.72

6.13

16.51

7.29

33.88

0.30

-9.25

2.90

16.77

1.97

-2.98

3.75

28.14

7.56

33.49

5.33

16.87

9.63

30.88

3.46

26.61

8.12

28.88

1.54

0.20

6.35

32.54

9.93

23.62

0.48

1.84

3.92

22.25

6.44

14.93

1.03

4.89

3.93

26.73

0.98

-2.17

0.26

19.34

2.98

16.40

2.72

12.69

6.10

14.60

4.22

17.68

1.79

11.03

8.12

36.27

2.61

18.39

1.92

-11.05

1.05

15.55

1.24

26.66

6.60

15.65

1.80

-0.38

0.23

-12.30

4.34

14.14

4.22

13.48

1.57

5.73

2.55

-2.74

3.52

9.83

4.92

17.10

4.87

8.54

6.47

18.29

0.52

17.84

7.11

24.86

0.23

-5.34

9.79

35.99

6.60

26.93

8.08

24.27

7.91

16.48

0.57

2.80

6.05

7.75

4.37

6.37

4.74

12.52

3.83

17.92

2.47

24.72

4.53

20.41

2.34

7.15

8.03

30.27

5.29

23.02

0.48

6.34

9.06

48.44

0.64

2.91

9.66

21.97

9.35

27.28

0.91

16.44

6.51

13.71

7.27

17.09

2.11

11.71

1.80

25.88

8.48

22.93

1.09

4.65

0.70

-15.03

8.41

20.04

3.90

13.93

1.70

7.84

0.20

-4.50

0.03

3.94

6.53

21.85

8.17

25.49

7.51

40.66

8.57

28.36

7.52

28.50

1.16

7.58

3.28

10.29

9.27

20.40

4.77

13.01

1.15

19.30

8.43

28.93

7.18

23.83

4.66

18.92

9.60

22.81

2.04

-2.56

9.85

13.96

5.12

26.63

5.74

12.88

2.02

21.92

1.58

5.41

4.32

11.75

7.05

10.98

5.15

23.70

9.39

35.62

3.80

13.68

5.94

33.30

8.19

28.82

6.25

20.04

0.26

-3.05

0.64

0.54

6.34

15.40

1.61

20.85

5.01

14.68

3.13

29.12

0.93

-6.67

4.79

12.45

5.19

15.90

1.75

6.54

2.69

6.26

1.38

15.68

5.75

17.34

1.47

6.31

2.21

-3.05

8.03

13.44

6.33

33.15

9.56

14.29

4.23

14.97

5.97

43.14

2.01

3.69

9.46

20.50

7.19

29.06

8.47

24.62

2.15

13.56

0.73

8.80

4.75

28.61

2.66

1.56

6.13

11.67

7.79

44.25

0.69

8.94

0.95

2.53

0.37

-1.09

5.40

13.44

3.89

22.48

2.44

21.12

5.40

15.28

3.48

3.89

4.85

9.16

9.54

39.05

7.24

35.67

9.40

33.74

0.40

5.89

0.14

-5.25

2.01

7.54

0.19

4.27

8.09

28.96

0.73

5.91

8.02

18.05

2.76

4.06

6.80

19.58

0.64

-7.55

4.14

4.43

4.83

9.17

5.31

16.70

2.83

-1.81

8.78

34.56

4.39

9.25

5.12

0.31

1.46

12.39

8.34

22.62

0.45

6.56

9.33

29.27

1.63

-15.12

9.35

30.89

3.08

5.45

4.00

19.93

1.52

1.93

3.18

9.58

5.28

19.17

3.59

5.95

2.32

11.44

7.61

41.26

4.73

16.88

7.04

17.54

6.21

20.99

4.12

14.68

8.12

31.71

6.09

29.71

7.68

41.62

5.03

26.47

5.84

24.29

2.33

8.72

8.64

33.95

9.65

34.50

9.96

35.04

4.59

5.61

2.44

9.69

3.34

4.87

3.19

16.14

3.27

39.79

7.22

31.03

8.67

21.93

1.76

24.95

3.04

12.51

3.97

29.82

2.64

8.45

9.86

19.98

0.67

27.93

9.41

18.60

9.14

19.83

8.64

27.05

9.30

19.72

9.22

46.95

0.59

14.34

7.44

50.89

6.04

22.56

1.79

16.94

7.93

37.68

0.16

-8.62

4.08

8.76

7.85

37.91

2.93

5.45

4.51

29.79

6.20

15.45

6.33

-0.68

1.97

-0.58

6.97

3.32

1.09

-3.21

1.66

17.68

5.26

13.54

1.36

0.68

9.05

21.40

2.94

10.83

0.64

12.71

3.64

6.75

8.58

26.61

0.23

13.75

6.01

19.64

0.98

8.76

0.67

-2.35

8.25

30.26

9.39

18.31

7.74

33.15

1.94

-12.77

2.87

6.09

0.75

3.03

6.27

8.97

3.64

18.89

0.66

0.97

4.64

21.24

5.25

20.27

7.69

38.49

6.78

8.77

7.66

35.23

3.53

26.01

6.60

30.92

1.62

16.12

9.88

29.26

2.10

14.16

8.68

33.73

1.41

11.27

4.27

7.52

2.18

17.15

5.10

18.76

3.17

5.29

3.09

11.42

2.06

-6.45

0.51

6.66

9.21

22.09

5.52

8.11

0.73

12.65

3.60

-1.68

1.73

-19.67

5.35

0.02

0.84

-7.27

9.26

43.90

2.48

-5.47

3.00

28.25

9.04

27.19

8.89

29.88

8.15

39.84

0.74

5.21

6.40

0.38

Task 1 Simulating a binomial random variable 1. A computer manufacturer claims that at most 2% of the products shipped are defective. A store receives shipments of 40 computers. (a) Assuming the worst case scenario, what fraction of shipments to the store will have at least one defective computer? (b) Using Excel's random number generation, simulate making 1000 shipments of 40 computers from the manufacturer described in (a), assuming that there are 2% defectives in each shipment. What fraction of the 1000 shipments contain at least one defective computer? How does this number compare with the probability you computed in a)? Task 2 Regression Analysis 2. The le bioarmls contains 400 computer generated bivariate data points labeled a: and y. (a) Construct a scatter plot of the data, including the regression line and R2 value. (b) Fill in the second row of the following table using the regression equation. Carry out the computations in Excel using suitable formulas. \"mun-l _--------- empirical estimate for f) (c) Fill in the third row by computing average y values using only data points whose a: value is near the number in row 1. For example, for o: = 1 you might estimate the regression value 3) from the data using the average of all 3; values for which the corresponding :5 is between 0.5 and 1.5. (Note: You may want to copy the data set onto a blank worksheet before manipulating it.) ((1) Should the values in row 3 be close to the values in row 2? Explain. Would you consider your results in line with these expectations? Hint: Use Regression Property 9.1 and Regression Property 9.2 on pages 161 and 162