Due date: 2016-12-01.

  1. OS3 Chapter 7 Exercises froms ection 7.5:

7.4) (a) strong But non linerar S shaped relation (b) strong. but Curiviliear relation or quadaratic relation (c) strong postive linear relation-fitting a linear model would be reasonable (d) weak. No relation exist-fitting a linear model would not be reasonable (e) weak -negative fitting a linear model would be reasonable (f) moderate -negative fitting a linear model would be reasonable

7.6) a) From the plot it is clear that there is a positive relationship between husbands and wives ages.

  1. There does not seem any relation betweeen husbands and wives heights.

  2. husbands and wives ages shows a stronger correlation, as an increased in one also shows increase in other’s age

  3. Siince the correlation is independent of change of origin, so there will be no change in the correlation between husbands’ and wives’ heights

7.24)

  1. Scatter plot shows that the relationship between number of calories and amount of carbohydrates is linear and positive.

  2. Explanatroty variable: Calories Response variable: Carbs (grams)

(c)Becuase scatter plot shows a linear relationship between teh variables.

(d)It seems that variables has positive linear relationship . And also residual plot does not shows any specific pattern. So least sqaure line can be fitted to these data.

7.30) The linear model will be Y=(B^0) + (B^1)X

  1. Intercept is the constant change in the model. So basically this means if set our predictor at 0 what will be the predicted value of Y. Here X=0 means Y_hat=-.357 meaning that if body weight were 0 number of heart weights will be -.357. Ofcourse this is worthless because weights cannot be negative. So it is better not to use the regression if X=0.

  2. Slope denotes the amount of change Y will record if keeping everything fixed we increse X by 1 unit. Here the slope is 4.034. Meaning the keeping everything else fixed if we increse the body weight by 1 unit then the annual number of murder permillion will be increased by 4.034.

  3. R^2 gives the proportion of variation explained by the model compraed to total variation in the model.64.66% of the total variation is explained by the model. R^2_adj gives a improved measure of model efficacy it is staged at 64.41% meaning this is a fairly good model.

  4. The correlation coefficient is simply the sqaure root of R^2 meaning high positive correlation between two

7.36 a) The slope of the equation is positive, so there is a positive relationship between the number of beer and blood alcohol content.

  1. The regression equation is (y^)=-0.01257+0.0180x Y is the BAC and X is the number of beers. The slope of the equation is 0.0180.

  2. H0:B1=0 H1:B1not equal to 0

Since 0.00<.05 the null hypothesis is rejected therefore there is sufficient evidence to conclude that the drinking more cans of beer is associated with an increase in blood alcohol.

  1. The correlation coeffcient is r=0.89 R2=(0.89)2=0.7921 79.21%

  2. Yes there will be relationship between number of drinks and BAC it will be as strong as the relationship found in the ohio state study.

  1. Consider an observational study about the infection risks of hospitals across the U.S, Hospitals were randomly sampled and a number of variables were measured. Interest lies in predicting the infection risk of hospitals. Perform simple linear regression with the explanatory variable of your choice and describe your analysis. Full sentences are required. You need at least the following items in your write up.

    1. A description of the data and the explanatory variable you chose.

    The data shows correlation between 7 variables the explanatory variable ive chosen is days spent in hospital.

    1. A correlation calculation.

    2. An appropriate plot to display the data with respect to your analysis.

    Would be a scatter plot

    1. A formal conclusion in both Statistics and in English.

    We can see that that over time the number of days spent in th hospital increase due to severity of illness.

    1. An interpretation of your model in context – intercept, slope.

    The slope of the line is positive so we can concluse that there is a correlation between number of days in hospital vs. days in hospital.

    1. The value your model predicts when the explanatory variable is equal to its mean and a sentence describing this value.

    2. The code used.