The data below contains information about the test results:

ID: student id

Hours: hours took

Score:test score (0 to 100)

Anxiety: anxiety level (0 to 100)

Gender: Male or Female

Question:

Let anxiety be your x-variable and test score be your y-variable.

Which of the following regression assumptions are met and why (in detail)?

Also, use R and show graphs to support your answers.

(a) Linearity

(b) Independence of errors

(c) Equal variance of errors (homoskedasticity)

(d) Normality of errors

(e) Bivariate normality

---- DATA ----

ID Hours Score Anxiety Gender

1 4 40 86.298 Male

2 11 65 88.716 Female

3 27 80 70.178 Male

4 53 80 61.312 Male

5 4 40 89.522 Male

6 22 70 60.506 Female

7 16 20 81.462 Female

8 21 55 75.82 Female

9 25 50 69.372 Female

10 18 40 82.268 Female

11 18 45 79.044 Male

12 16 85 80.656 Male

13 13 70 70.178 Male

14 18 50 75.014 Female

15 98 95 34.714 Male

16 1 70 95.164 Male

17 14 95 75.82 Male

18 29 95 79.044 Female

19 4 50 91.134 Female

20 23 60 64.536 Male

21 14 80 80.656 Male

22 12 75 77.432 Male

23 22 85 65.342 Female

24 84 90 56.116 Female

25 23 30 71.79 Female

26 26 60 81.462 Female

27 24 75 63.73 Male

28 72 75 27.46 Female

29 37 27 73.402 Female

30 10 20 89.522 Male

31 3 75 89.522 Female

32 36 90 75.014 Female

33 43 60 43.58 Male

34 19 30 82.268 Male

35 12 80 79.044 Male

36 9 10 79.044 Female

37 72 85 37.132 Male

38 10 7 81.462 Male

39 12 5 83.074 Female

40 30 85 50.834 Male

41 15 20 82.268 Male

42 8 45 78.238 Female

43 34 60 72.596 Male

44 22 70 74.208 Female

45 21 50 75.82 Female

46 27 25 70.984 Male

47 6 50 97.582 Male

48 18 40 67.76 Male

49 8 80 75.014 Male

50 19 50 73.402 Female

51 0 35 93.552 Female

52 52 80 58.894 Female

53 38 50 53.252 Female

54 19 49 84.686 Male

55 23 75 89.522 Female

56 11 25 71.79 Female

57 27 65 82.268 Male

58 17 80 69.372 Male

59 13 50 62.118 Male

60 42 70 68.566 Female

61 4 40 93.552 Male

62 8 80 84.686 Female

63 6 10 82.268 Male

64 11 20 81.462 Female

65 7 40 82.268 Male

66 15 40 91.134 Male

67 4 70 91.94 Female

68 28 52 86.298 Female

69 22 50 72.596 Male

70 29 60 63.73 Female

71 2 80 63.73 Male

72 16 60 71.79 Female

73 59 65 57.282 Male

74 10 15 84.686 Female

75 13 85 84.686 Male

76 8 20 77.432 Female

77 5 80 82.268 Female

78 2 100 10 Male

79 38 100 50.834 Female

80 4 80 87.91 Male

81 10 10 83.88 Male

82 6 70 84.686 Female

83 68 100 20.206 Female

84 8 70 87.104 Male

85 1 70 83.88 Female

86 14 65 67.76 Male

87 42 75 95.97 Female

88 13 85 62.118 Female

89 1 30 84.686 Male

90 3 5 92.746 Male

91 5 10 84.686 Female

92 12 90 83.074 Female

93 19 70 73.402 Male

94 2 20 87.91 Female

95 19 85 71.79 Male

96 11 35 86.298 Male

97 15 30 84.686 Female

98 23 70 75.82 Male

99 13 55 70.984 Female

100 14 75 78.238 Female

101 1 2 82.268 Male

102 9 40 79.044 Male

103 20 50 91.134 Female