Question

1. A sample of 10 adult men gave the following data on their heights and weights.

Height (inches)	X	62	62	63	65	66	67	68	68	70	72
Weight (pounds)	Y	120	140	130	150	142	130	135	175	149	168

1. (2 points) Generate the scatter plot of this data and graph the regression line in your plot. Include a picture of this graph and explain your impression of how well the line fits the data.

The X is the horizontal axis and shows the explanatory variable and the Y axis is the response. So in this scatter plot shows the man’s weight in response his height.

2. (1 point) State the equation of the regression line. Y= a + bX

3. (2 points) Find r (correlation coefficient). Interpret the value of r in the context of

      this problem.   r= 0.6559800965 This number shows a positive correlation between weight and height.

4. (2 points) Find the coefficient of determination, r². Explain what it means in the context of this problem. r²= 0.65598006965 65.60% of the variation in weight is explained by variation in height
   
5. (1 point) Provide examples of other lurking variables that may have an effect on weight   besides height. Other variables that may affect weight could be family history (genetics), eating habits, or activity level.

6. (1 point) Predict the weight of a man whose height is 60 inches.

7. (1 point) Predict the height of a man whose weight is 160 pounds.

F and G is what I am having problems with.

Answer 1

a)

Height vs Weight 200 180 160 y= 3.3526x - 78.377 140 120 Weight 100 80 60 40 20 0 60 62 64 66 68 70 72 74 Height

b)

We will be applying the Linear regression model here, it can be done by using the function =LINEST(y_value, x_value, TRUE, TRUE) where y_values contain values of Weight here and x_values have Height values.

Select 5 rows and 2 columns and then write the formula in the first cell and after that, press Shift + Ctrl + Enter.    

The equation comes out to be -
Y = -78.4 + 3.35*X  

c)

The r value of 0.655 shows a positive strong relationship between the two variables.

d)

The coefficient of determination comes out to be 0.43, which means the change in Weight can be explained 43% by the height.

e)

Other variables that may affect weight could be family history (genetics), eating habits, or activity level.

f)

When X = 60

Y = -78.4 + 3.35*X  

Y = -78.4 + 3.35*60 = 122.8

g)

When Y = 160

160 = -78.4 + 3.35*X

238.4/3.35 = X

A B H 1 X Y 2 62 120 3 62 140 4 63 130 5 65 150 6 66 142 7 67 130 correlation 0.65598 CORREL(B2:B11, A2:A11) 8 68 135 9 68 175 10 70 149 slope intercept 3.352595 -78.3771 1.363844 90.52784 0.43031 13.7809 6.042722 8 1147.593 1519.307 11 72 168 12 w 14 15 Y = -78.4 +3.35*X 16 17