Question

Please I need the answers for question 6 and 7 :

6. Elementary school teachers are concerned about "screen time for children. Specifically, they worry that too much time with television, computers, pads, and smart phones is interfering with reading ability. They decide to do a statistical study. They randomly choose some elementary school children from their district, and interview them and their families to determine the amount screen time, on average, per week, for each child. They also record the children's reading scores on standard reading ability test (a) What is the response variable? What is the main predictor of interest? What are (b) Download the data in tvread.txt and determine the relationship between the (c) The covariate "grade of child" is also included in the data set. Include this variable the hypotheses to be tested? response and main predictor. Interpret the results in the context of the problem in the model and interpret the results in the context of the problem. (d) The teachers are confused about the difference in the results when the covariate is included compared with when it is not. Carefully explain why the results are different, including nice graphics in your explanation. 7. Art teachers in a large city are dismayed by reduced spending in the art programs in school and possible future cuts. To demonstrate the importance of spending on the arts, they randomly select eighty middle schools in the city. For each school, they have the annual art expenditure per student (in dollars) and the average score on the state-mandated standardized exam. They plot the standardized exam score against art expenditure, and observe an increasing trend. Download their data from Canvas (a) Confirm the observation of an increasing trend by fitting a line to the data. Pro- vide a p-value for their conjecture, and state the null and alternative hypotheses associated with the p-value. Interpret the slope estimate in the context of the problem (b) The neighborhoods that the schools serve have been categorized into groups of "low," "middle" and "high" socioeconomic status (SES). This variable is also in- cluded in the dataset, where 1-low, 2-middle, and 3-high SES. Include this variable in your model. Describe the relationship between exam score and art expenditure, when the SES is controlled for in the model (c) The teachers are confused about the difference in the results when the covariate is included compared with when it is not. Carefully explain why the results are different, including nice graphics in your explanation.

Answer 1

Calculations for Regression coefficients: bo and b XY X-Art expenditure Y - score 32 86 37 84 37 65 40 57 40 103 41 78 41 124 41 64 Sample Size: nlength (X) it-0,1..n-1 Mean value of X: -77.988 n-1 Mean value of Y: 85.213 n- 1 SSXY=Σ(x-x-).(Y-Y-)=29361.213 SSXtD(X-X-109210.988 Sample slope numberator: 44 50 44 47 44 54 n -1 Sample slope denominator: SSX : Σ (Xi-X)-109210