Question

Please summarize what you can conclude from this model. What interpretations can you make about the slope and intercept? Would you feel comfortable using your regression equation to make predictions?

I chose to see if there is a relationship between the variables: height and weight. The explanatory variable is height and the response variable is weight. I am only using the heights and weights of 10, 20 year old females to make sure there aren't any lurking variables.

Test Subject	Body weight in lbs	height in inches
Female 1	140	5.6
Female 2	150	5.5
Female 3	130	5.3
Female 4	133	5.7
Female 5	140	5.0
Female 6	120	5.2
Female 7	139	5.7
Female 8	144	5.7
Female 9	144	5.8
Female 10	134	5.6

The regression equation is y = 1.323X + 51.241 with a correlation coefficient of .1640.

Answer 1

> weight=scan("clipboard")
Read 10 items
> weight
[1] 140 150 130 133 140 120 139 144 144 134
> height=scan("clipboard")
Read 10 items
> height
[1] 5.6 5.5 5.3 5.7 5.0 5.2 5.7 5.7 5.8 5.6
> model=lm(weight~height)
> summary(model)

Call:
lm(formula = weight ~ height)

Residuals:
Min 1Q Median 3Q Max
-13.2972 -4.6133 0.2471 3.7545 12.7323

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 64.48 58.27 1.107 0.301
height 13.23 10.56 1.253 0.246

Residual standard error: 8.244 on 8 degrees of freedom
Multiple R-squared: 0.164,   Adjusted R-squared: 0.05951
F-statistic: 1.57 on 1 and 8 DF, p-value: 0.2457

Interpretations

The regression equation is

weight=64.48 + 13.23 * height

from the coefficient table the pvalue of height is greater than 0.05, we may accept the null hypothesis and conclude that the height is insignificant variable in the model i.e, it is not sufficient variable to find the approximate weight.

Also, here  Multiple R-squared: 0.164 that is only 16.40% variation in weight is explained by the variable height, and R-squared is also low, hence it suggest that height is not enough variable to predict the weight.

now F-statistic: 1.57 on 1 and 8 DF, p-value: 0.2457 here p value of model is grater than 0.05 level of significance we may accept the null hypothesis and conclude that the the model is insignificant.

>cor(weight,height)
[1] 0.4049824
here the correlation between height and weight is positive, that is as height increases weight also increases.